LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 

Class 


CONCRETE  BRIDGES 


AND 


CULVERTS 


NET  BOOK— This  Book  is  supplied 
to  the  trade  on  terms  which  do  not 
admit  of  discount. 

THE  MYRON  C.  CLARK  PUBLISHING  CO. 


Graduate  of  Toronto  University 


CHICAGO    AND    NEW    YORK 

THE  MYRON  C.  CLARK  PUBLISHING  Co. 


LONDON 

E.  &  F.  N.  SPON,  LTD.,  57  Haymarket 
1909 


a    < 


CONCRETE  BRIDGES 

I  AND 

CULVERTS 


FOR  BOTH 
RAILROADS  AND  HIGHWAYS 


BY 

H.  GRATTAN  TYRRELL 

Civil  Engineer 
Graduate  of  Toronto  University 


CHICAGO    AND    NEW    YORK 

THE  MYRON  C.  CLARK  PUBLISHING  Co. 


LONDON 

E.  &  F.  N.  SPON,  LTD.,  57  Haymarket 

1909 


COPYRIGHT  1909 

BY 
H  GRATTAN  TYRRELL 


PREFACE. 

Bridges  of  solid  concrete  are  superior  to  those  of 
any  other  material.  They  are  as  permanent  as  stone, 
and  have  a  less  cost.  Masonry  bridges  and  aque- 
ducts built  by  the  Romans  are  still  standing,  and 
some  of  them  in  use.  A  few  old  cast  iron  bridges  re- 
main, dating  back  a  century  or  more,  but  a  majority 
of  the  modern  ones  built  of  wrought  iron  and  steel 
have  a  very  limited  existence.  Forty  years  ago,  steel 
bridges  were  believed  to  be  permanent  structures, 
but  it  is  now  well  known  that  they  do  not  generally 
last  longer  than  from  twenty  to  thirty  years. 

Solid  concrete  bridges  are  superior  to  those  in 
which  reinforcing  metal  is  required  for  resisting 
tensile  stresses  in  the  arch  ring.  Continuous  water- 
soaking  reduces  the  adhesion  of  concrete  to  steel  by 
about  100  per  cent,  and  the  effect  of  shocks  and  vi- 
brations also  tends  to  destroy  the  bond.  It  fre- 
quently occurs  that  cracks  develop,  sufficiently  large 
to  admit  water,  and  when  water  and  moisture  reach 
the  reinforcing  metal,  it  is  then  only  a  few  years  be- 
fore the  metal  is  destroyed  by  rust. 

An  old  wire  suspension  bridge  that  recently  failed, 
was  examined  and  reported  on  by  the  writer,  and  it 
was  found  that  failure  occurred  because  of  the  rust- 
ing and  breaking  of  the  wire  cables  embedded  in 
the  anchorage.  When  the  bridge  was  built,  it  was 
doubtless  considered  that  the  cables  when  painted 

194738 


iv  PREFA  CE. 

and  embedded  in  concrete,  were  secure  against  cor- 
rosion. Sufficient  caution  was  not  taken  to  exclude 
moisture  from  the  anchorages,  and  the  bridge  failed 
as  stated  above,  by  the  rusting  and  breaking  of  the 
embedded  metal.  It  is  evident,  therefore,  that 
the  most  enduring  bridges  are  those  of  solid  mason- 
ry, where  no  metal  is  required. 

Many  of  the  largest  masonry  bridges  built  in  re- 
cent years,  have  arch  rings  built  of  solid  concrete, 
without  reinforcing  metal  for  resisting  direct  stress- 
es. Details  of  some  of  these  are  given  in  Table  Xo. 
I.  Even  in  arches  with  reinforcement,  the  best  de- 
signers are  now  proportioning  the  arch  rings,  so  the 
line  of  pressure  for  uniform  loads  will  at  all  times 
fall  within  the  middle  third  of  the  arch  ring,  and 
require  no  reinforcing  for  these  loads. 

In  the  Engineer's  Pocket-Book,  Mr.  Trautwine 
makes  the  following  statements: — "Nearly  all  the 
scientific  principles  which  constitute  the  foundation 
of  Civil  Engineering,  are  susceptible  of  complete 
and  satisfactory  explanation  to  any  person  who 
really  possesses  only  such  knowledge  of  arithmetic 
and  natural  philosophy,  as  is  taught  to  boys  in  pub- 
lic schools.  The  little  that  is  beyond  this,  may  safe- 
ly be  intrusted  to  the  savant.  Let  them  work  out 
the  results,  and  give  them  to  the  engineer  in  intelli- 
gible language.  We  can  afford  to  take  their  word, 
because  such  things  are  their  specialty.  The  object 
has  been  to  elucidate  in  plain  English,  a  few  im- 
portant elementary  principles,  which  the  savants 
have  enveloped  in  such  a  haze  of  mystery,  as  to 


PREFA  CE  v 

render  pursuit  hopeless  to  any  but  a  confirmed  math- 
ematician." 

Several  complete  and  very  comprehensive  trea- 
tises have  already  been  written,  covering  the  mathe- 
matical theory  of  arches,  and  as  far  as  this  feature 
of  the  subject  is  concerned,  there  is  little  left  to 
be  desired. 

Tn  the  preparation  of  this  manual,  the  effort  has 
therefore  been  made,  to  as  far  as  possible  eliminate 
mathematical  formulae,  and  to  present  the  subject 
in  the  simplest  possible  manner.  Only  such  material 
is  given  as  is  directly  required  in  the  design  and 
construction  of  ordinary  concrete  or  masonry  arches, 
so  it  will  be  unnecessary  for  the  busy  engineer  to 
spend  valuable  time  and  thought  in  the  perusal  and 
study  of  obstruse  mathematical  treatises.  Practi- 
cing engineers  have  but  little  time  for  mathematical 
investigation,  and  generally  must  accept  formulae 
as  given  to  them  by  others. 

A  real  need  for  this  book  is  believed  to  exist,  ow- 
ing to  the  increased  use  of  concrete  bridges. 

The  designs  and  data  tables  for  culverts  and  tres- 
tles are  original  with  the  author,  and  are  here  pre- 
sented for  the  first  time.  They  are  the  result  of 
his  own  practice  in  the  design  and  construction  of 
railroad  structures. 

In  the  preparation  of  this  manual,  I  have  received 
valuable  assistance  from  my  wife,  Maude  K.  Tyrrell, 
a  graduate  of  the  Chicago  Art  Institute,  and  ex- 
perienced in  architectural  design.  I  am  indebted 
also  to  the  following  gentlemen  for  assistance  as 


vi  PREFACE. 

noted : — To  Julius  Kahn  for  two  views  of  concrete 
trestles,  to  Whitney  Warren,  Architect,  for  views 
of  the  proposed  Hudson  Memorial  Bridge, 
to  Messrs.  Lea  and  Felgate  for  views  and 
drawings  of  the  Rocky  River  Bridge,  to  George 
S.  Webster  for  a  photograph  of  the  Walnut  Lane 
Bridge  at  Philadelphia,  and  to  H.  HawTgood  for  the 
illustrations  and  drawings  of  the  Santa  Ana  Bridge. 
1  am  also  indebted  to  the  Engineering  News  for 
drawings  of  the  proposed  Hudson  Memorial  Bridge, 
the  Spokane  and  the  Grand  Avenue  Bridges,  and  to 
the  Engineering  Record  for  two  drawings  of  the 
Rocky  River  Bridge  and  drawing  of  Edmondson 
Avenue  Bridge. 

H.  G.  Tyrrell. 
Evanston,  Illinois. 
November,  1909. 


\ 


TABLE  OF  CONTENTS. 
PART  I.— PLAIN  CONCRETE  ARCH  BRIDGES. 

Page. 

Composition i 

Advantages   of    Masoniy    Construction 1 

Uncertainty    of    Masonry    Arches 4 

Form    g 

Hinged  Arches 10 

Position   of   Springs n 

Abutment    Piers n 

Height   of    Bridge 12 

Rise  arid  Span 12 

Crown    Thickness 14 

Thickness  of   Crown   Filling 16 

Spandrels    16 

Various  Forms  and  How  to  Draw  Them 20 

Ellipse    20 

Multi-Centered  Arch.     Three  Centers 20 

Multi-Centered   Arch.     Five   Centers 22 

Parabolic  Arches 23 

Hydrostatic   and   Geostatic   Arches 24 

Selection  of  Most  Suitable  Form 27 

External  Loads  and  Forces 29 

Mathematical  Theory  of  the  Arch 32 

Stability    Requirements 33 

Ultimate  Values 34 

Working    Units 35 

Line  of  Resistance.     Full  Loading 36 

Line  of  Resistance.     Partial  Loading 45 

Point   of    Rupture 50 

Determination   of   Arch  Thickness 51 

Backing   52 

Waterproofing   and    Drainage 52 

Intermediate    Piers 53 

Abutment    Piers 54 

Abutments    55 

Foundations   58 

Expansion  60 

Surface   Finish 60 

Cost    of    Concrete   Arch    Bridges 63 

vii 


viii  CONTENTS. 

Page. 

Design  for  a  60  ft.  Arch  Bridge 65 

Uneven    Loading 68 

Required   Arch   Area 69 

Intermediate    Piers 69 

Abutment    Piers 70 

Illustrations  of    Concrete   and   Masonry   Bridges 71 

Ponte  Rotto,  Rome 74 

Bridge  of  Augustus  at  Rimini,  Italy 76 

Hudson  Memorial  Bridge,  New  York  City 78 

Auckland,  New  Zealand,  Bridge 80 

Rocky  River  Bridge,  Cleveland,  Ohio 81 

Walnut   Lane    Bridge,    Philadelphia 85 

Connecticut   Avenue    Bridge,   Washington 87 

Big  Muddy  River  Bridge,  Illinois 89 

Santa   Ana   Bridge,   California 91 

Table   of    Concrete   Arch    Bridges 95 

PART    II— REINFORCED    CONCRETE    ARCH 

BRIDGES    100 

Historical   Outline 102 

Advantages  of  Reinforced  Concrete 106 

Adhesion  and   Bond 108 

Metal   Reinforcement Ill 

Reinforcing    Systems 117 

Concrete    Composition 120 

Loads   121 

Units — Ultimate  and  Working 125 

Theory  of  Arches 128 

General    Design 136 

Hinged  Arches 140 

Ribbed    Arches 141 

Intrados    Form 145 

Spandrels    147 

Piers   and    Abutments 148 

Costs  of  Reinforced  Concrete  Arch  Bridges 150 

Estimating    154 

Approximate  Estimating  Prices 155 

Table   of    Approximate    Quantities 158 

Potomac  Memorial   Bridge  Design 159 

Jamestown  Exposition  Bridge 161 

Franklin  Bridge,  Forest  Park.  St.  Louis 161 

Jefferson  St.  Bridge,  South  Bend,  Indiana 16 

Gary,  Indiana,  Bridge 163 

Como  Park  Foot  Bridge,  St.  Par.l 163 

Boulder    Faced   Bridge,    Washington 166 

Grand  Rapids   Arch   Bridge 166 


CONTENTS.  ix 

Page. 

Bridge  at  Venice,  California 169 

Garfield  Park  Bridge,  Chicago 169 

Stein-Tenf en   Bridge.  Switzerland 173 

Table  of  Reinforced  Concrete  Arches 174 

PART  III.— HIGHWAY  BEAM  BRIDGES. 

Comparison  of  Arch  and  Beam 181 

Beam   Bridges 183 

Method  of  Design 185 

PART      IV.— CONCRETE      CULVERTS      AND 

TRESTLES    189 

Required   Size   of    Culvert   Opening 191 

Reinforced   Concrete    Box   Culverts 194 

Loads     195 

Economic  Length  for  Slabs  and  Slab-Beams 198 

Reinforced  Concrete  Slab  Table  No.  VI 198 

Single  Box  Culverts,  Slab  Type,  Table  No.  VII 205 

Double  Box  Culverts,  Slab  Type,  Table  No.  VIII 207 

Single  Box  Culverts,  Beam  and  Slab,  Table  No.  IX 209 

Double  Box  Culverts,  Beam  and  Slab,  Table  No.  X 211 

Comparative  Culvert  Costs,  Various  Forms 213 

Other  Common  Culvert  Forms 216 

Culvert  Data,  Table  No.  XI 227 

Concrete    Railroad    Trestles 228 

Economic    Span    Lengths 230 

Description  of  Various  Trestle  Designs 230 

Design    A 230 

B 235 

C 235 

D 238 

E 238 

F 238 

G  and  H 242 

Comparative  Trestle  Costs 242 


x  LIST  OF  ILLUSTRATIONS. 

PART  I. 

SOLID  CONCRETE  ARCH  BRIDGES. 

Frontispiece — Potomac   Memorial   Bridge,   Washington. 

Fig.  Page. 

1.  Ellipse    20 

2.  Three   Centered   Arch 21 

3.  Five  Centered  Arch 22 

4.  Parabolic    Arch 23 

5.  Hydrostatic    Arch 26 

0.       Comparison  of  Above  Curves 27 

7.  Pressure  Curve,  Full  Loads 38 

8.  Alternate  Pressure  Curve,  Full  Loads 44 

9.  Pressure   Curve,   Partial   Loads 46 

10.  Design  for  Twin  Arches 48 

11.  Abutments    57 

12.  Design  for  Railroad  Bridge 62 

13.  Ponte   Rotto,   Rome 73 

14.  Bridge  of  Augustus  at  Rimini,  Italy 75 

15.  Hudson   Memorial   Bridge 7t 

16.  Monroe  St.  Bridge,  Spokane,  Wash 79 

17.  Rocky  River  Bridge,  Cleveland 82 

18.  Rocky  River  Bridge,  Cleveland 83 

19.  Rocky  River  Bridge,  Cleveland ; 84 

20.  Walnut  Lane  Bridge,  Philadelphia 86 

21.  Connecticut   Avenue   Bridge,   Washington 88 

22.  Big  Muddy  River  Bridge,  Illinois 90 

23.  Santa  Ana  Bridge,  California 92 

24.  Santa  Ana  Bridge,  California 93 

PART  II. 

25.  Design  for  Concrete  Highway  Bridge 99 

26.  Theory   of    Arches 134 

27.  Grand  Avenue  Bridge  Design,  Milwaukee 143 

28.  Jamestown    Exposition    Bridge 160 

29.  Franklin   Bridge,   Forest  Park,   St.   Louis.... 162 

30.  Jefferson  Street  Bridge,  South  Bend,  Indiana 164 

31.  Gary,   Indiana,   Bridge 165 

32.  Como  Park  Foot  Bridge,  St.  Paul 167 

33.  Boulder  Faced  Bridge.  Washington 168 

34.  Grand   Rapids   Arch    Bridge 170 

35.  Bridge  at  Venice,  California 171 

36.  Garfield  Park  Bridge,  Chicago 172 

PART  III. 

37.  Three  Span  Beam  Bridge 180 

38.  Single  Span  Slab  Bridge 182 

39.  Single  Span  Beam  Bridge 184 


LIST    OF    ILLUSTRATIONS.  xi 

PART  IV. 

Fig.  Page. 

40.  Richmond,    Va.,    Trestle 188 

41.  Augusta,    Ga.,    Trestle t 190 

42.  Relative  Cost  of  Slab  and  Beams 200 

43.  Single    Box    Culverts,    Slabs 202 

44.  Double    Box    Culverts,    Slabs 203 

45.  Single   Box   Culverts,   Beams 204 

46.  Culvert    Cost    Chart 213 

47.  Culvert    Cost    Chart 217 

48.  Concrete   Box   Culverts,   Slabs 218 

49.  Concrete  Box   Culverts,   Beams 220 

50.  Beam  Top  Box  Culverts 221 

51.  Concrete  Box  Culverts,  Slab  Type 222 

52.  Concrete  Box  Culverts,  Beam  and  Slab , 223 

53.  Rail  Top  Culverts 224 

54.  Reinforced  Concrete  Arch 225 

55.  Beam  Top  Culvert 226 

56.  Parabolic    Arch    Culvert 226 

57.  Sewer  Type  Arch  Culvert 227 

58.  Concrete  Trestle,  Design  A,  Rail  Top. 231 

59.  Concrete  Trestle,  Design  B,  Beam  Top 233 

60.  Concrete  Trestle,  Design  C,  Steel  Beams 234 

61.  Concrete  Trestle,  Design  D,  Beam  Top 236 

62.  Concrete  Trestle,  Design  E,  Slabs  with  Rods 237 

63.  Concrete  Trestle,  Design  F,  Beam  and  Slabs 239 

64.  Concrete  Trestle,  Design  G,  Slabs 240 

65.  Concrete  Trestle,  Design  H,  Beam  and  Slab 241 

66.  Concrete  Trestles,   Comparative   Costs 243 


PART  I. 

PLAIN   CONCRETE   ARCH   BRIDGES. 

Composition. 

Masonry  arches  were  formerly  built  almost  en- 
tirely of  brick  and  stone.  In  recent  years,  however, 
owing  to  the  increased  production  of  cement  and 
modern  methods  of  making  concrete,  including  the 
crushing  of  stone  and  the  mixing  and  handling  of 
materials,  a  large  number  of  our  modern  bridges  are 
built  of  concrete.  Brick  arches  lack  the  bond  of 
stone.  They  are  usually  laid  in  concentric  rings,  the 
edge  of  the  brick  appearing  in  the  soffit  of  the  arch. 
Occasionally  the  bricks  have  been  laid  dry,  and 
grout  run  in  to  fill  solid  all  cavities.  As  brick  is 
a  softer  material  than  stone  or  concrete,  its  use  does 
not  appear  to  have  any  special  advantage.  All 
masonry  arches,  whether  built  of  brick  or  stone  as 
block  structures,  or  made  of  concrete  in  a  solid 
monolith,  carry  their  loads  entirely  through  com- 
pression in  the  arch  ring,  and  while  the  mortar 
joints  would  doubtless  resist  considerable  tension  if 
so  required,  no  reliance  should  be  placed  on  the  ten- 
sile strength  of  such  joints. 

Advantages  of  Masonry  Construction. 

Tn  many  respects  a  masonry  arch  is  superior  to 
either  a  steel  bridge  or  a  combination  of  steel  and 
concrete.  Some  of  these  advantages  may  be  enu- 
merated as  follows  :  —  Cement  hardens  with  age,  and 
consequently  the  older  the  bridge,  the  stronger  it 
becomes.  Therefore,  if  it  successfully  sustains  its 
first  test  load  it  will  always  be  secure.  This 
condition  is  reversed  in  steel  structures,  which 


CONCRETE   BRIDGES   AND   CULVERTS. 

deteriorate  with  age  through  the  action  of 
rust  and  the  loosening  of  rivets  and  pins.  As 
travel  increases,  concrete  bridges  become  stronger 
to  support  it;  neither  is  there  any  yearly 
expense  for  painting  or  other  maintenance. 
They  can  generally  be  built  from  local  ma- 
terial, and  largely  by  local  and  unskilled  labor. 
The  building  and  completion  of  such  bridges 
is  not  dependent  on  mills,  shops,  or  the  operation 
of  trusts,  as  is  frequently  the  case  with  steel  struc- 
tures. In  this  respect,  concrete  bridges  have  an 
advantage  over  those  of  combined  steel  and  concrete, 
for  in  the  latter  case,  it  is  frequently  necessary  to 
await  the  convenience  of  the  shops  for  the  reinfor- 
cing steel.  A  consideration  that  should  appeal  to 
the  purchasers  of  bridges  is,  that  local  labor  and  ma- 
terials for  concrete  structures  can  usually  be  secured 
and  used,  and  the  money  expended  by  a  municipal- 
ity goes  back  to  its  own  people,  instead  of  going  to 
distant  points  in  payment  for  manufactured  steel. 

Arches  in  general,  which  form  is  usually  adopted 
for  masonry  bridges,  present  a  more  substantial  and 
pleasing  appearance  than  can  be  secured  by  any 
form  of  truss,  even  though  an  arched  truss  be  con- 
sidered, for  in  a  truss,  the  outline  of  the  arch  is  not 
so  evident  as  in  a  solid  structure.  For  railroad 
bridges  the  arch  of  solid  concrete  is  superior  to  the 
reinforced,  in  that  its  greater  weight  and  mass  more 
readily  absorb  the  vibrations  and  shocks  due  to  the 
passage  of  heavy  trainloads  and  engines.  Concrete 
bridges  require  no  floor  renewals  as  steel  bridges 


PLAIN  CONCRETE  ARCH  BRIDGES.  3 

frequently  do,  and  they  will  generally  cost  from  10 
to  30  per  cent  less  than  stone.  They  are  fire  proof 
and  have  no  steel,  either  in  the  form  of  principals  or 
reinforcement,  to  rust.  They  can  be  widened  at  any 
time  without  tearing  down  the  original  bridges,  as 
must  be  done  with  bridges  of  wood  and  steel. 

Bridges  of  solid  concrete  are  particularly  suitable 
for  permanent  railroad  structures.  Many  railroad 
companies  are  realizing  their  superior  advantages 
and  are  replacing  their  steel  bridges  with  new  ones 
of  masonry,  and  while  these  concrete  bridges  are 
frequently  reinforced  with  steel,  the  main  arches 
are  in  most  cases,  designed  to  resist  only  compres- 
sive  stresses,  with  no  need  for  steel  in  tension  except 
to  better  unite  the  arch  and  to  prevent  cracking  from 
change  of  temperature.  Many  iron  and  steel  rail- 
road bridges  in  America  have  been  replaced  two  or 
three  times  by  heavier  steel  ones  during  the  past 
thirty  or  forty ,  years,  in  order  to  renew  worn  out 
structures  or  to  provide  for  heavier  loads.  When 
it  is  remembered  that  several  masonry  bridges  in 
Europe  that  were  built  2,000  years  ago,  are  still 
standing  and  in  use,  it  is  evident  economy  for  per- 
manent roadways,  to  rebuild  ordinary  spans  in  ma- 
sonry. Views  of  two  old  Roman  bridges  are  shown 
on  subsequent  pages.  Ponte  Rotto  at  Rome,  shown 
on  page  73,  was  first  completed  in  the  year  142  B.  C., 
and  while  it  has  been  damaged  several  times  by 
floods,  owing  to  its  unfortunate  location,  three  arch 
spans  still  remain  in  good  condition.  The  Bridge  of 
Augustus  at  Rimini,  supposed  to  have  been  built 


4  CONCRETE   BRIDGES   AXD   CULVERTS. 

about  14  A.  D.,  during  the  reign  of  Emperor  Augus- 
tus, has  five  arch  spans.  The  piers  are  very  heavy 
and  support  semicircular  arches.  The  bridge  is  fine- 
ly ornamented,  is  still  in  good  condition  and  in  use 
at  the  present  time.  A  view  is  shown  on  page  75. 

Uncertainty  of  Masonry  Arches. 

As  compared  with  steel  frames,  the  design  of  ma- 
sonry arches  is  uncertain.  The  hypotheses  upon 
which  the  design  is  based  are  only  approximate  as- 
sumptions, and  when  constructed,  the  action  of  the 
arch  under  loads  is  unreliable.  In  the  former  case, 
with  single  truss  systems  and  truss  lines  meeting 
in  points,  with  working  unit  values  closely  known 
by  long  series  of  experiments  in  both  tension  and 
compression,  the  designing  of  such  frames  has  be- 
come almost  an  exact  science.  It  is  different  with 
masonry  arches,  as  their  conditions  under  loads  are 
too  little  known  to  arrive  at  any  exact  method  for 
proportioning  them.  Moreover,  even  if  these  con- 
ditions were  more  definitely  known,  the  same  incen- 
tive for  reducing  the  quantities  of  material  does  not 
exist  in  masonry  as  in  steel  structures,  because  of 
the  comparative  cheapness  of  masonry.  Some  of  the 
indefinite  factors  in  the  design  of  masonry  arches  are 
as  follows : — 

(1)  The  condition  and  amount  of  the  external 
forces  are  not  definitely  known.  For  instance,  in 
an  arch  with  spandrel  earth  filling,  the  amount  of 
the  conjugate  horizontal  pressure  of  the  earth  against 
the  extrados  of  the  arch  is  comparatively  unknown. 


PLAIN  CONCRETE  ARCH  BRIDGES.  5 

If  the  filling  were  a  liquid,  the  external  pressure 
Avould  then  be  normal  to  the  extrados  and  its 
amount  would  be  definite.  This  condition  does  not 
ordinarily  exist,  and  the  nearest  approach  to  liquid 
pressure  is  from  spandrel  filling  of  clean  dry  sand. 
It  is  well  known  that  earth  filling,  which,  when  new- 
ly placed,  will  stand  at  no  greater  slope  than  one 
and  one-half  to  one,  will  after  it  becomes  set,  sup- 
port itself  for  a  time,  at  any  rate,  with  almost  verti- 
cal faces.  Hence,  conjugate  pressure  which  may 
have  existed  at  first,  while  the  arch  was  under  con- 
struction, may  vanish  later.  In  the  case  of  an  arch 
under  a  deep  embankment,  it  is  plainly  evident  that 
such  an  arch  does  not  support  the  entire  weight  of 
earth  filling  above  it,  as  the  earth  to  some  extent 
arches  itself.  The  case  of  a  tunnel  arch  is  an  excel- 
lent example.  Such  an  arch  is  proportioned  to 
carry  only  a  small  part  of  the  load  above  it,  de- 
pending upon  the  nature  of  the  overlying  material. 
Further,  where  the  masonry  is  continuous  over  the 
piers,  especially  where  a  large  amount  of  backing 
is  used,  the  material  tends  to  cantilever  itself  from 
the  piers,  and  thereby  relieve  the  arch  of  much  of 
its  load,  or  if  the  amount  of  backing  and  filling 
above  it  be  large,  these  materials  may  to  a  great  ex- 
tent arch  themselves  from  pier  to  pier,  and  thereby 
relieve  the  real  masonry  arch.  The  external  span- 
drel walls  may  also  act  as  arches  and  carry  a  con- 
siderable load.  The  above  remarks  apply  to  bridge 
arches.  In  the  case  of  arches  in  buildings,  the  con- 
dition of  the  external  loads  or  forces  is  even  more  in- 


6     CONCRETE  BRIDGES  AND  CULVERTS. 

definite.  Take,  for  example,  the  case  of  an  arch  car- 
rying a  wall  load  above  it.  It  is  customary  to  con- 
sider that  the  arch  carries  the  entire  weight  of  such  a 
Avail.  The  fact,  however,  is  that  an  unbroken  wall 
supports  itself  almost  entirely,  by  acting  as  a  mason- 
ry beam  or  by  arching  itself,  and  the  only  portion 
supported  by  the  arch  is  a  triangular  piece  of  ma- 
sonry directly  above  it.  This  is  true  for  a  wall 
without  openings.  When  openings  occur  the  above 
consideration  will  be  effected,  depending  upon  the 
location  of  the  openings.  If  they  occur  in  such  po- 
sitions as  to  evidently  interfere  with,  and  destroy 
the  beam  or  arch-action  of  the  superimposed  ma- 
sonry, then  the  entire  weight  of  masonry  may  come 
on  the  arch.  There  are  many  bridge  arches  now 
standing  that  would  doubtless  fail,  were  they  sub- 
jected to  the  entire  weight  of  the  materials  above 
them.  After  striking  center,  the  arch  itself  has  set- 
tled, and  much  of  the  imposed  load  is  transferred  to 
the  piers  by  the  cantilever  or  arch  action  of  the 
backing  and  fill,  or  the  arch  action  of  the  spandrel 
walls. 

(2)  Another  unknown  factor  in  the  design  of  ma- 
sonry arches  is  the  strength  of  masonry.  Experi- 
ments have  been  made  principally  on  small  sam- 
ples tested  in  machines  with  pressures  normal  to 
surface,  all  of  which  conditions  are  quite  different 
to  those  of  actual  arches  under  loads.  The  material 
is  then  concentrated  in  bulk,  with  pressures  inclined 
to  bearing  surfaces  and  with  loads  more  or  less  of  a 
vibratory  nature. 


PLAIN  CONCRETE  ARCH  BRIDGES.  1 

(3)  It  is  usually  assumed  by  engineers  and  an 
alysts,  that  the  joints  of  block  structures  such  as 
masonry  arches  will  resist  no  tensile  stress.     This 
is  a  precaution  on  the  side  of  safety,  but  may  be 
far  from  true.     With  a  rich  quality  of  concrete,  we 
know  that  properly  formed  points  will  actually  re- 
sist considerable  tension,  provided  they  remain  in- 
tact. 

(4)  The  position  of  the  line  of  resistance  in  the 
arch  is  not  definitely  known.    This  is  largely  due  to 
the  continuity  of  the  arch  at  the   center,  and  the 
square  bearings  at  the  piers  or  springs.     To  obviate 
this  difficulty,  some  European  engineers  have  built 
masonry   arches   with    hinges    at    the     crown   and 
springs,  thus  fixing  the  position  of  the  line  of  resist- 
ance at  these  points,  but  in  America  such  provisions 
are  not  generally  used. 

(5)  Imperfect  workmanship  in  the  cutting  of  the 
stones  and  the  fitting  of  the  joints  is  another  factor 
causing  the  actual  line  of  resistance  to  move  from 
its  supposed  position  to  a  different  one,  where  the 
joints  come  to  a  firm  bearing. 

(6)  The  removal  of  the  arch  center  and  the  set- 
tling  of  the   arch   to   its   permanent   position,   also 
effects  to  some  extent  the  theoretical  considerations. 

It  appears  therefore  that  any  effort  at  ultra  re- 
finement in  arch  design  is  a  waste  of  energy,  for  the 
actual  conditions  existing  in  a  completed  structure 
may  not  even  approximate  those  assumed. 


8  CONCRETE   BRIDGES   AND   CULVERTS. 

Form. 

The  form  or  general  outline  is  the  first  considera- 
tion in  the  design  of  a  masonry  arch.  Semicir- 
cular and  semi-elliptical  arches,  commonly  known  as 
full  centered  arches,  spring  from  horizontal  beds, 
while  segmental  arches  spring  from  inclined  beds 
called  skewbacks.  The  old  Roman  arches  were  near- 
ly all  semicircular.  In  bridges  and  viaducts  where 
piers  are  used,  full  centered  arches  or  those  which 
spring  from  horizontal  beds,  are  preferable  to  seg- 
mental arches  springing  from  inclined  beds,  for  the 
reason  that  full  centered  arches  produce  a  less  over- 
turning moment  on  the  pier,  and  their  attachment 
to  the  piers  with  horizontal  beds  is  simpler  than 
with  inclined  springs.  The  thrust  on  piers,  however, 
depends  upon  the  rise  of  arch,  which  is  not  neces- 
sarily the  distance  from  spring  to  center  intrados. 
The  effective  rise  is  the  vertical  height  from  spring 
to  crown,  measured  on  the  linear  arch  or  line  of 
pressure  and  any  minor  curve  joining  the  arch  soffit 
to  the  pier,  is  not  effective  and  must  not  be  con- 
sidered as  part  of  the  rise.  Segmental  arches  have  a 
shorter  curve  than  elliptical  for  the  same  span,  or 
for  the  same  length  of  soffit  the  segmental  arch 
results  in  a  wider  span.  For  small  spans  such  as 
commonly  used  for  culverts,  segmental  arches  con- 
tain from  25  to  40  per  cent  less  masonry  than  semi- 
circular arches,  though  common  practice  makes  the 
segmental  arch  ring  10  to  25  per  cent  thicker  than 
the  semicircular.  For  fluid  pressure  the  proper 
form  of  arch  is  the  semicircle.  The  effect  of  earth 


PLAIN  CONCRETE  ARCH  BRIDGES.  9 

fill  or  other  loads  at  the  haunches,  tends  to  raise  the 
line  of  pressure  to  the  approximate  form  of  an  el- 
lipse, while  the  effect  of  a  uniform  load,  such  as  the 
weight  of  earth  fill  and  pavement  above  the  crown, 
together  with  a  uniform  live  load,  tends  to  depress 
the  line  of  pressure  to  the  approximate  form  of  a 
parabola.  The  combined  effect  of  these  two  loadings 
is  to  bring  the  line  of  pressure  more  nearly  to  the 
segment  of  a  circle.  ,  The  most  economical  form  is 
a  linear  arch  of  the  given  span  for  the  required 
loading,  in  which  the  thickness  is  proportional  to 
the  thrust.  In  such  an  arch  every  part  of  the  cross- 
section  would  be  stressed  alike.  One  authority  rec- 
ommends that  the  form  of  intrados  for  arches  with 
earth  filled  haunches  be  midway  between  a  circular 
segment  and  ellipse.  Any  variation  from  regular 
curves  that  is  sufficient  to  be  apparent  to  the  eye,  is 
a  violation  of  a  principle  of  design  and  should  not 
be  permitted.  The  many  three  and  five  centered 
flat  arches  already  in  existence  are  sufficient  to  clear- 
ly prove  the  utter  failure  of  such  forms  to  produce 
artistic  or  satisfying  effects.  If  multi-centered  flat 
arches  must  be  used,  they  should  be  drawn  from  as 
many  centers  as  possible.  Three  and  five  centered 
arches  are  suitable  when  the  form  approaches  a 
semicircle. 

An  economical  form  of  arch  with  cantilever  brack- 
ets at  the  ends  has  lately  been  built  over  the  Yermil- 
lion  River  at  Wakeman,  Ohio.  The  bridge  has  cross 
walls  with  open  spandrels,  a  clear  span  of  145  feet, 
and  end  cantilever  brackets  37  feet  long.  The  meth- 


10          COXCRETE  BRIDGES   AND   CUU7ERTS. 

od  necessitates  the  use  of  reinforcing  metal  at  the 
floor  level  for  the  purpose  of  tying  the  brackets  to 
the  main  span.  A  somewhat  similar  plan  was  adopt- 
ed in  the  Topeka  bridge,  but  in  the  latter  case  the 
concrete  cantilevers  were  for  retaining  walls  only. 
The  cantilevers  were  tied  together  with  rods  to  pre- 
vent spreading  from  the  pressure  of  the  earth  filling. 
In  the  case  of  arches  such  as  culverts  under  high 
embankments,  the  segmental  arch  with  its  horizon- 
tal thrust  is  economical.  The  arch  thrust  resists  and 
counteracts  the  earth  pressure  on  the  sidewalk  from 
without. 

Hinged  Arches. 

A  practice  that  has  long  been  followed  in  Europe, 
is  to  provide  stone  or  metal  hinges  at  the  crown  and 
springs.  The  use  of  such  hinges  locates  definitely 
the  position  of  the  line  of  pressure  at  these  points, 
and  thereby  removes  one  of  the  common  uncertain- 
ties of  masonry  bridges.  Hinges  are  particularly 
desirable  where  the  nature  of  the  soil  is  yielding  or 
uncertain.  Any  lateral  movement  of  the  abutments 
causes  the  arch  to  sink  at  the  crown  when  the  centers 
are  removed,  and  such  sinking  produces  cracks  that 
are  unsightly  and  possibly  dangerous.  When  hinges 
are  used,  the  joints  are  filled  in  solid  writh  cement 
mortar,  after  the  centers  are  removed  and  the  arch 
ring  has  assumed  its  final  position.  For  additional 
loads,  the  entire  area  of  both  hinges  and  mortar  fill- 
ing will  then  be  available  for  resisting  arch  thrusts. 


PLAIN  CONCRETE  ARCH  BRIDGES.  11 

Position  of  Springs. 

The  arch  springs  should  be  located  as  near  to 
the  foundation  as  conditions  will  permit.  This  will 
reduce  the  overturning  effect  on  the  pier  to  a  mini- 
mum, and  produce  a  more  stable  construction.  Some 
of  the  conditions  governing  the  position  of  the 
springs  are  as  follows :  Over  streams  the  spring  must 
be  sufficiently  high  to  allow  ample  water  way,  and 
clearance  for  the  passage  of  boats  or  drift ;  over 
roads  or  highways  the  springs  must  be  sufficiently 
high  to  provide  proper  head  room  and  clearance  for 
the  passage  of  pedestrians  and  vehicles,  and  over 
railroads,  for  the  passage  of  cars.  In  the  last  case, 
there  must  be  a  clear  head  room  of  at  least  21  feet 
at  a  distance  of  five  feet  from  the  face  of  piers. 
This  allows  clearance  for  the  largest  box  cars  and 
additional  space  for  trainmen  on  the  roof. 

Abutment  Piers. 

For  long  bridges  or  viaducts  with  a  series  of 
arches,  abutment  piers,  or  those  of  sufficient  thick- 
ness to  resist  the  pressure  of  a  single  arch,  should  bo 
placed  at  frequent  intervals.  Where  the  spring  lina 
is  located  so  near  the  foundation,  that  piers  need  not 
be  excessively  thick,  it  may  be  desirable  to  have  all 
piers  of  the  abutment  type.  Then,  during  the 
course  of  construction,  the  spans  may  be  built  inde- 
pendently and  false  work  removed  when  desired, 
without  reference  to  the  adjoining  spans,  or  after 
the  completion  of  the  bridge  if  one  span  should  be 
destroyed  by  flood  or  other  cause,  the  other  spans 


12          CONCRETE   BRIDGES  AND   CULVERTS. 

would  still  remain  intact.  If  all  piers  in  an  arch 
viaduct  are  of  the  ordinary  type,  to  support  vertical 
loads  only,  and  one  span  should  be  destroyed,  then 
the  remaining  spans  would  also  fall,  one  after  the 
other  in  succession,  by  the  overturning  of  successive 
piers. 

Height  of  Bridge. 

In  most  cases,  the  height  of  the  bridge  or  level  of 
the  roadway  will  be  previously  determined.  In  some 
cases,  however,  the  floor  grade  may  be  varied  more 
or  less  by  grading  the  approaches  to  suit  other  con- 
ditions. It  may  be  that  money  spent  in  raising  the 
approaches  and  the  level  of  the  bridge  floor,  will  be 
saved  many  times  in  the  cost  of  the  masonry. 

Rise  and  Span. 

The  span  is  the  clear  distance  betwreen  vertical 
faces  of  piers  or  abutments,  and  the  rise  is  the 
height  of  crown  above  springs,  measured  on  the 
line  of  pressure,  and  not  on  the  arch  intrados. 
Curves  joining  flat  arches  to  piers  are  not  part  of 
the  effective  rise. 

The  length  of  span  and  rise  of  arch  will  be  among 
the  first  considerations.  In  many  cases,  the  natural 
conditions  will  determine  one  or  both  of  these  di- 
mensions. If  the  bridge  is  short,  a  single  span  may 
be  sufficient.  If  it  spans  a  street  or  rapid  stream, 
where  piers  are  impracticable,  the  conditions  will 
require  only  one  span.  In  long  viaducts,  the 
dividing  of  such  a  structure  into  spans  of  proper 
length  is  an  important  matter.  The  economic  span 


PLAIN  CONCRETE  ARCH  BRIDGES.  13 

length  depends  chiefly  upon  the  total  height  of 
structure  above  foundations.  Generally,  high  struc- 
tures require  longer  spans,  and  lower  structures, 
shorter  spans.  For  steel  bridges  with  vertical  reac- 
tions, the  economic  length  of  span  for  various 
heights  is  well  known  or  may  easily  be  determined, 
but  with  arches  there  are  other  considerations.  The 
usual  practice  is  as  follows : — Place  the  springing 
lines  on  the  piers  down  to  the  lowest  point  possible 
consistent  with  the  necessary  clearance,  and  after 
allowing  for  the  thickness  of  the  arch  ring  and  fill- 
ing at  the  crown,  draw  in  spans,  the  length  of  which 
are  from  two  to  five  times  the  rise  of  the  arch,  pref- 
erence being  given  to  spans  of  twice  the  rise  or  to 
semicircular  arches.  Certain  other  conditions,  how- 
ever, may  determine  the  length  of  span.  For  exam- 
ple, in  a  long  viaduct  over  railroad  yards,  it  may 
be  desired  to  span  a  certain  number  of  tracks  with 
each  arch,  or  to  have  as  few  piers  as  possible  to  in- 
terfere with  additional  tracks  or  switches.  In  that 
case,  the  length  of  span  may  be  fixed  arbitrarily  re- 
gardless of  the  rise  or  height  of  bridge. 

Tn  fixing  the  lengths  of  a  series  of  arch  spans,  the 
Romans  made  those  spans  nearest  to  the  center  of 
the  river,  longer  than  the  shore  spans.  The  plan  is 
still  in  general  use,  and  it  has  the  merit  of  causing 
the  span  at  a  distance  from  the  shore  observer,  to 
appear  at  least  as  long  as  the  nearer  ones.  When 
a  uniform  span  length  is  used,  the  effect  of  perspec- 
tive is  to  cause  those  spans  near  to  the  river  center 


14          CONCRETE   BRIDGES   A\'D   CULVERTS. 

which  should  be  of  greater  importance,  to  appear 
shorter  than  they  really  are. 

To  balance  the  pier  thrust  from  unequal  spans, 
the  shorter  one  may  have  a  smaller  rise  with  greater 
earth  filling  and  consequently  greater  loads. 

Several  of  the  large  railroad  companies  have  re- 
cently adopted  standard  segmental  culvert  arches 
having  a  rise  of  one-fifth  the  span.  In  many  other 
bridges  this  proportion  is  exceeded,  especially 
where  natural  or  other  conditions  govern.  General- 
ly speaking  it  will  be  found  cheaper  to  make  long 
spans  with  few  piers,  provided  sufficient  rise  is 
available. 

Crown  Thickness. 

In  the  preliminary  design  it  is  necessary  to  know 
approximately  the  required  crown  thickness  or  depth 
of  keystone,  and  also  the  amount  of  earth  filling 
over  the  crown,  to  determine  the  remaining  distance 
from  crown  to  spring  or  the  available  height  for 
the  rise  of  arch.  The  crown  thickness  may  be  found 
approximately  by  reference  to  tables  of  existing 
arches,  or  from  some  reliable  empirical  formula. 
Trautwine's  formula  for  such  thickness  is  as  fol- 
lows, a  development  of  the  formula  for  various 
spans  and  rises  being  given  in  the  Engineer's  Pocket 
Manual. 


Depth  of  key  in  feet=  -\Radius-fhalf  span  +.0  ftt 

4 

The  above  is  for  the  tirst  class  cut  stone  work, 
either  circular  or  elliptical.  For  second  class  ma- 
sonry, increase  the  results  from  the  above  formula 


PLAIN  CONCRETE  ARCH  BRIDGES.  15 

by  one-eighth,  for  brick,  by  one  third;  for  large 
elliptical  arches  some  engineers  increase  also  the 
above  values  by  one-third. 

Rankine's  rule  for  croAvn  thickness  is: — 

For  single  spans  A'.12  Radius 


For  several  spans  -*  .17  Radius 

It  becomes  necessary  therefore  to  determine  the 
radius  at  the  crown.  This  can  be  done  graphically. 
The  crown  radius  for  an  ellipse  can  be  found  as 
described  later  and  shown  in  Figure  2.  It  is  com- 
mon practice  with  small  segmental  arches  to  make 
the  arch  ring  from  10  to  25  per  cent  thicker  than 
semicircular  ones. 

The  crown  thickness  may  also  be  found  approxi- 
mately by  first  determining  the  approximate  crown 
thrust.  This  is  easily  computed  by  finding  the  cen- 
ter bending  moments  for  all  loads,  the  same  as  for  a 
beam,  and  then  dividing  by  the  rise,  or  the  approxi- 
mate crown  thrust  ma^  be  found  from  Navier's 
formula,  T— />r,  where  T  is  the  crown  thrust,  p  the 
average  pressure  per  square  unit  on  the  arch,  and  r 
the  radius  of  arch  at  crown.  It  will  be  noted  that 
the  proper  value  for  the  crown  thrust  is  that  one 
which  produces  equilibrium  about  the  point  of  rup- 
ture, and  not  about  the  springs. 

The  experience  of  the  Writer  in  using  Trautwine's 
tables  of  sizes  and  quantities  for  masonry  arches  is 
that  Trautwine's  figures  are  about  one-third  larger 
than  the  best  practice  now  in  use  by  the  large  rail- 
road systems  for  the  design  of  concrete  arches. 


16          CONCRETE  BRIDGES   AND   CULVERTS. 
Thickness  of  Crown  Filling. 

An  assumed  depth  for  this  filling  is  required  as 
noted  above,  in  order  to  determine  the  available 
height  for  the  rise  of  the  arch.  For  highway 
bridges,  a  depth  of  filling  including  the  pavement, 
of  from  one  to  two  feet  will  be  sufficient,  but  for 
railroad  structures  a  greater  depth  is  necessary  in 
order  to  form  a  cushion  for  the  ties  and  absorb  and 
distribute  the  shock  from  passing  trains.  For  this 
purpose  a  depth  of  from  two  to  four  feet,  or  ordi- 
narily of  two  feet  below  the  ties  will  be  sufficient. 
To  secure  this  cushion  effect,  the  filling  in  some  re- 
cent concrete  railroad  bridges  has  been  as  great 
as  five  feet. 

Spandrels. 

Bridge  spandrels  are  either  filled  solid  with  earth 
held  in  place  by  side  retaining  walls,  or  the  floor 
over  the  spandrels  is  supported  on  a  series  of  in- 
terior walls  and  arches,  which  may  or  may  not  ap- 
pear on  the  exterior.  The  solid  earth  filling  is  gen- 
erally used  for  small  spans  and  flat  arches.  But  for 
large  arches  and  especially  semicircular  ones,  the 
open  construction  will  be  cheaper.  In  certain  cases 
of  comparatively  flat  arches,  even  where  it  would 
be  more  expensive  than  solid  filling,  the  open  spin- 
drel  construction  may  be  desirable  for  the  purpose 
of  reducing  the  load  on  the  foundations.  This 
was  the  case  with  an  elliptical  arch  bridge  recently 


PLAIN  CONCRETE  ARCH  BRIDGES.  17 

built  by  the  Illinois  Central  Railroad  Company  over 
Big  Muddy  River,  containing  three  spans  of  140  feet 
each,  with  30  feet  rise.  It  was  found  that  the  open 
spandrel  construction  reduced  the  loading  on  the 
piles  by  about  six  tons  per  pile.  Which  one  of 
these  methods  to  use  in  any  particular  case,  can  be 
determined  by  making  comparative  designs  and  es- 
timating the  costs.  In  many  cases,  however,  the 
choice  can  be  made  by  inspection. 

By  building  open  chambers  crosswise  of  the  bridge 
and  having  the  openings  appear  on  the  spandrel 
faces,  a  design  is  produced  that  presents  a  lighter 
appearance  and  at  the  same  time  shows  plainly  the 
plan  of  construction.  When  a  heavier  and  more 
massive  appearance  is  desired,  then  the  side  wralls 
may  be  used  and  all  spandrel  openings  closed.  In 
large  arches  approaching  the  semicircular  form,  if 
open  spandrels  are  used  and  the  interior  spandrel 
walls  run  parallel  writh  the  axis  of  the  bridge,  these 
walls  then  act  as  backing  and  produce  the  necessary 
conjugate  thrusts  on  the  haunches  below  the  points 
of  rupture.  The  need  of  providing  for  necessary 
conjugate  thrusts  is  important  and  must  not  be  over- 
looked. Cross  spandrel  walls  and  open  chambers  or 
arcades  may  be  used  above  the  point  of  rupture, 
but  below7  that  point  the  construction  must  be  solid. 
This  type  of  construction  is  well  illustrated  by  the 
Connecticut  Avenue  bridge  at  Washington,  shown 
on  page  88. 


18          CONCRETE   BRIDGES  AND   CULVERTS. 

An  improved  method  of  designing  spandrels  is  il- 
lustrated in  the  Piney  Creek  Parabolic  Arch  bridge 
in  Washington.  The  floor  slabs  are  carried  on  an 
interior  system  of  beams  and  columns  supported  on 
the  arch  ring,  and  the  spandrels  are  enclosed  with 
thin  curtain  walls.  A  design  similar  to  this  for  a 
segmental  arch  was  prepared  by  Mr.  Thacher  for 
the  Bellefield  bridge  in  Schenley  Park,  Pittsburg. 
This  system  is  a  very  economical  one  and  has  the 
advantages  of  leaving  the  interior  construction  open 
at  all  times  for  inspection,  and  of  producing  a  less 
amount  of  load  in  the  spandrels  for  the  arch  to 
carry.  The  curtain  walls  are  also  thinner  than  re- 
taining walls  for  earth  filling  and  cost  proportion- 
ately less,  and  the  pavement  may  be  laid  at  once 
without  waiting  for  the  filling  to  settle.  When  the 
pavement  is  laid,  there  will  never  be  any  liability 
of  the  road  settling,  as  often  does  occur  when  pave- 
ment is  laid  on  earth  filling,  even  though  such  fill- 
ing be  well  rammed  and  permitted  to  settle  a  long 
time  before  laying  the  roadway. 

The  use  of  the  open  spandrel  construction  with 
either  cross  walls  or  columns  avoids  any  uncertainty 
in  reference  to  horizontal  conjugate  pressure  from 
spandrel  filling,  and  also  prevents  water  collecting 
and  soaking  into  the  arch  masonry.  When  it  is  de- 
sired to  secure  a  greater  diversity  in  design,  the  face 
walls  may  be  omitted  and  the  interior  arcade  or 
colonnade  construction  artistically  treated  for  the 


PLAIN  CONCRETE  ARCH  BRIDGES.  19 

purpose  of  producing  a  more  pleasing  architectural 
effect.  In  comparing  the  relative  costs  of  colon- 
nade and  arcade  construction  for  spandrels,  en- 
closed column  construction  will  generally  be  found 
the  cheaper,  for  the  beams  and  columns  may  be  left 
rough,  and  the  spandrel  curtain  wall  only  will  need 
a  finished  surface.  Cross  arcade  construction  has 
the  economy  of  small  dead  load,  but  all  open  span- 
drel walls  are  exposed  to  view  and  may  require  fin- 
ished surfaces  or  possibly  architectural  treatment. 
Open  chambers  may  be  enclosed  at  the  top,  either 
by  means  of  arching  or  by  using  flat  slabs  of 
stone  or  reinforced  concrete.  The  upper  surface  is 
then  waterproofed  by  applying  a  layer  of  rich  mor- 
tar and  surfacing  with  neat  cement,  on  top  of  which 
is  poured  a  layer  of  tar  or  pitch.  The  surface  may 
then  be  leveled  with  gravel  and  sand,  and  the  pave- 
ment laid. 

Another  reason  for  selecting  either  the  solid  or 
the  open  spandrel  type  is  for  the  purpose  of  adjust- 
ing the  imposed  loads  on  the  arch  to  the  form 
selected.  This  may  be  necessary  to  secure  stability 
and  will  be  considered  later  under  the  head  of  load- 
ing. In  designing  the  side  spandrel  walls  to  retain 
earth  filling  the  usual  rules  for  retaining  walls  will 
apply.  Practice  is  to  make  the  thickness  of  such 
walls  at  the  base  40%  of  the  height.  They  should 
be  firmly  doweled  or  otherwise  secured  to  the  arch 
masonrv, 


20          CONCRETE  BRIDGES   AND   CULVERTS. 
Various  Forms  and  How  to  Draw  Them. 

The  forms  adopted  for  the  intrados  of  masonry 
arch  bridges  are  generally  circular,  segmental, 
elliptical,  or  multi-centered.  These  four  types  can 
be  reduced  to  two,  circular  and  elliptical,  for  the  seg- 
mental arch  is  merely  a  segment  of  a  circle,  and  the 
multi-centered  arch  is  merely  an  approximate  ellipse. 
The  two  general  forms  are,  therefore,  the  circu- 
lar and  the  elliptical. 


Methods  of  drawing 
the  ellipse  and  the 
multi-centered  curve 
are  as  follows: 

Ellipse. 

Let   AD  and  CD 

be  the  semi-major 
and  semi-minor  axes 
of  an  ellipse  at  right 
angles  to  each  other. 
Draw  circular  arcs 


Fig.  1 


with  radii  AD  and  CD,  respectively.  From  points 
where  a  common  radius  intersects  the  two  circular 
arcs,  draw  vertical  arid  horizontal  ordinates.  The  in- 
tersection of  these  ordinates  gives  points  on  the  ellipse. 

Multi-Centered  Arch — Three  Centers. 

These  curves  are  sometimes  called  basket-handled 
arches.     The  method  of  drawing  a  three-centered 


PLAIN  CONCRETE  ARCH  BRIDGES. 


21 


c  arch  is  as  follows  : 
Let  AD  and  CD 
be  the  semi-major 
and  semi-minor 
axes,  respectively, 
of  a  true  ellipse. 
The  form  of  the 
true  ellipse  is  first 
drawn  by  the 
method  given 
above.  This  is 
showrn  in  Figure  2 
by  the  full  line. 
The  approximate 
form  is  then 
o  drawn  as  follows : 
Assume  any  two  equal  distances  CB  and  AE  less 
than  half  of  the  semi-minor  axis.  Join  BE  and  bisect 
the  line  BE  at  F.  Through  F  draw  a  perpendicu- 
lar to  BE,  intersecting  the  line  CD  at  0.  The  two 
points  0  and  E  will  be  centers  of  two  circular  arcs 
which  will  form  an  approximate  ellipse.  By  first 
selecting  the  position  of  the  point  E  so  the  circular 
arc  described  from  E  as  center  will  conform  as 
closely  as  possible  with  the  true  ellipse,  satisfactory 
curves  will  easily  be  found.  The  full  line  on  Figure 
2  shows  the  true  ellipse  and  the  dotted  line  the  ap- 
proximate. 


Fig.  2 


22 


CONCRETE  BRIDGES  AND   CULVERTS. 


Five-Centered  Arch. 

A  method  for  drawing  a  five-centered  arch  is  as 
follows : — 

In  order  to  check  on  the  work,  it  is  advisable  to 
first  draw  the  form  of  the  true  ellipse  by  the  method 

given  above.  In 
Figure  3  the  two 
curves  so  closely 
correspond  that 
only  one  can  be 
shown.  On  the 
[transverse  axis 
AO  draw  the 
rectangle  AGCO, 
equal  in  height 
to  the  semi-minor 
axis  OC  of  the 
ellipse,  and  draw 
the  diagonal  AC. 
From  G  draw  a 
line  GHD  per- 
pendicular to  AC 
and  intersecting 
the  center  line 
CO  of  the  span  produced  at  D.  From  0  as  cen- 
ter, with  radius  OC,  draw  the  circular  quadrant 
as  shown.  Describe  the  semicircle  ARL  and 
produce  the  line  OC  to  its  intersection  with  the 
semicircle  at  L.  From  O  as  center,  describe  the 
arc  at  M  with  radius  equal  to  CL,  andD  as  center  de- 


PLAIN  CONCRETE  ARCH  BRIDGES. 


23 


scribe  arc  rtM,  with  DM  as  radius.  On  the  axis  AO 
lay  off  AN  equal  to  OL.  Then  from  II  as  center, 
with  radius  HN.  describe  the  arc  Na,  cutting  Ma 
at  a.  The  three  points  IT,  a  and  D,  with  correspond- 
ing ones  in  the  other  quadrant  are  the  five  desired 
centers  from  which  to  draw  the  approximate  ellipse. 
This  method  of  drawing  a  five-centered  arch  as  ap- 
proximate to  an  ellipse  must  not  be  confounded  with 
the  method  given  later  for  drawing  a  hydrostatic 
arch.  The  crown  radius  of  the  ellipse  will  be  less 
than  the  corresponding  radius  of  the  hydrostatic 
arch. 

Parabolic  Arch. 

The  parabola  is  not  frequently  used  in  masonry 
bridges,  but  the  formula  for  drawing  it  is  given.  It 

is  as  follows  : — 

*       3        *        '  o      The  various  let- 

ters refer  to  di- 
mensions shown  in 
the  accompanying 
Figure  4. 

„  =  *»& 
F*i 

The  line  OR  is  divided  into  any  number  of 
convenient  equal  parts,  which  are  numbered  1,  2,  3, 
etc.,  beginning  at  the  point  nearest  O.  Then  to 
find  the  value  of  y,  for  the  various  ordinates  x,  the 
numbers  1,  2,  3,  etc.,  may  be  inserted  in  the  above 
equation  for  values  of  x,  and  the  total  number,  which 
in  the  illustration  is  6,  will  be  inserted  for  the  value 


24          CONCRETE   BRIDGES   AXD   CULVERTS. 

of  a.     The  upper  line  in  Figure  4  shows  the  corres- 
ponding form  for  a  true  ellipse. 

A  very  simple  graphical  method  of  drawing  the 
parabola  is  to  lay  off  on  the  vertical  line  RS  the 
same  number  of  equal  divisions  as  drawn  on  the 
horizontal  axis  OR,  and  from  0  draw  radiating  lines 
to  the  various  division  points  on  the  vertical  axis 
RS.  From  the  various  points  on  the  horizontal  line 
OR  draw  vertical  lines  intersecting  the  radiating 
lines  from  0.  The  points  at  which  these  vertical 
lines  intersect  the  radiating  lines  are  points  on  the 
required  parabolic  curve. 

Hydrostatic  and  Geostatic  Arches. 

In  selecting  the  most  suitable  form  for  the  in- 
trados  of  an  arch,  the  following  consideration  of 
the  above  two  forms  of  curves  will  be  serviceable. 
The  hydrostatic  arch  is  the  form  of  a  linear  arch 
under  varying  pressures  which  are  always  normal 
to  the  line  of  arch.  This  condition  corresponds  to 
that  of  an  arch  submerged  below  the  surface  of 
water.  As  the  depth  below  the  surface  increases 
these  normal  pressures  increase  proportionately,  and 
as  the  external  pressures  are  always  normal  to  the 
surface,  the  amount  of  pressure  in  the  arch  is  con- 
stant, and  is  equal  to  the  produce  of  the  external 
pressure  at  the  point  by  the  radius  of  curvature. 
The  equation  is  T=pr,  and  is  known  as  Navier's 
Principle.  Since  the  essential  principle  of  the  hy- 
drostatic arch  is  that  fluid  pressure  is  normal  to 
the  surface,  the  thrusts  at  all  points  of  the  arch 


PLAIN  CONCRETE  ARCH  BRIDGES.  25 

ring  are,  therefore,  constant,  and  cannot  vary  with- 
out the  application  of  oblique  or  tangential  pres- 
sures. Since  T  is  constant,  r  will  vary  directly  as  /> 
These  radii  may  be  found  for  varying  depths  below 
water  level,  and  the  corresponding  curve  plotted. 
It  will  be  noted  that  the  thrust  T  at  the  crown,  is 
equal  to  the  total  horizontal  pressure  on  the  ex- 
trad  os  of  half  the  arch. 

Ordinarily,  however,  arches  are  subjected  to  earth 
pressure  rather  than  water.  The  external  forces 
fire,  therefore,  no  longer  normal  to  the  extrados 
o£  the  arch,  but  bear  a  relation  thereto,  depending 
on  the  nature  of  the  overlying  material.  In  the  case 
of  earth  or  gravel  filling,  having  an  angle  of  repose 
of  one  and  one-half  to  one,  it  is  known  that  the  hori- 
zontal pressure  exerted  against  vertical  surfaces  is 
about  one-third  of  the  weight  of  the  material  above 

the  point  under  consideration.  The  formula  is  H=-^-. 

o 

The  linear  arch  supporting  a  filling  of  clean  dry 
sand  would  be  the  true  form  of  the  geostatic  arch. 
If  p  is  the  horizontal  intensity  of  force  in  the 
hydrostatic  arch,  and  p'  the  corresponding  force  in 
the  geostatic  arch,  then  p=Cpf.  It  will  be  seen, 
therefore,  that  the  geostatic  arch  bears  the  same 
relation  to  the  hydrostatic  arch  as  the  ellipse  does 
to  the  circle.  A  linear  geostatic  arch  may,  there- 
fore, be  drawn  for  any  assumed  value  of  C,  such  as 
3,  which  experiments  show  to  be  about  the  right 
factor  for  earth  or  gravel  filling.  In  drawing  this 
linear  arch  all  the  vertical  co-ordinates  of  the  hydro- 


CONCRETE  BRIDGES  AND   CULVERTS. 


static  arch  are  retained,  and  conjugate  pressures 
changed  according  to  the  formula  p=Cpf.  For 
arches  under  heavy  banks  of  earth  the  geostatic 
arch  can  be  drawn  from  the  hydrostatic  arch.  If 
the  height  is  fixed,  the  form  of  curve  and  proper 
width  can  be  found  to  properly  withstand  the  earth 
pressure.  For  bridges,  these  principles  are  useful 
chiefly  for  arches  under  high  embankments. 

In  his  book  on  Civil  Engineering,  page  420,  Ran- 
kine  gives  the  following  approximate  method  for 
drawing  the  form  of  a  hydrostatic  curve  about  five 
centers  by  means  of  circular  arcs.  The  two  radii  r' 

"]?"  and  r°  are  first  computed 
from  the  accompanying 
formula.  This  fixes  two 
of  the  centers  and  the 
third  is  found  at  E  as 
shown.  The  equations 
for  radii  are  as  follows :— 

*  5 


r>=1- 


30  a 

DE  ==  AF— BD 

/     a3 


x  —  a  - 


PLAIN  CONCRETE  ARCH  BRIDGES. 


27 


In  Figure  5,  let  FB  be  the  half  span  and  FA  the 
rise  of  the  proposed  arch.  Make  AC=r°,  and 
BD— r',  the  radius  of  curvature  at  the  crown  and 
springing  as  calculated  from  the  above  formulae. 
Then  C  will  be  one  of  the  centers  and  D  another. 
About  D,  with  the  radius  DE,  describe  a  circular 
arc,  and  about  C,  with  radius  CF,  describe  another 

circular  arc.  Let 
E  be  the  point  of 
intersection  o  f 
these  arcs.  The 
points  D,  E  and  C 
will  be  the  re- 
quired centers. 

Many  semi-ellip- 
tic arches  ap- 
proach very  near- 
ly the  form  of  a 
hydrostatic  arch. 
A  comparison  be- 
tween Rankine's  approximate  curve  and  the  true  one 
are  shown  in  Figure  6.  The  upper  or  outside  curve 
is  the  approximate  curve  as  given  by  Rankine.  The 
center  curve  is  the  true  hydrostatic  arch  plotted 
from  a  succession  of  radii,  and  the  inside  curve  is  a 
true  ellipse. 

Selection  of  the  Most  Suitable  Form. 

Full  centered  arches,  either  circular  or  elliptical, 
produce  the  least  overturning  moment  on  the  piers, 
and  wTill  generally  require  less  pier  masonry  than 


Fig.  6 


28         CONCRETE  BRIDGES  AND   CULVERTS. 

segmental  arches.  If  the  arch  thrusts  against  nat- 
ural rock  skewbacks  or  abutments,  the  amount  of 
such  thrust  is  then  a  matter  of  little  importance  as 
far  as  the  abutment  is  concerned.  The  attachment 
of  segmental  arches  to  piers  usually  requires  tilted 
beds  to  bring  the  joints  at  right  angles  to  the  line 
of  pressure.  This  is  a  condition  that  does  not  occur 
in  full  centered  arches.  In  flat  ellipses  the  pier 
thrust  is  greater  than  with  semicircular  arches,  the 
position  of  thrust  approaching  more  nearly  that  of 
a  segmental  arch.  It  has  already  been  shown  that, 
for  arch  culverts  carrying  heavy  earth  banks,  the 
segmental  form  of  arch  will  be  more  effective  and 
less  expensive.  It  produces  heavy  thrusts  on  the 
abutments,  which  thrusts  counteract  the  inward 
pressure  of  the  earth  on  the  side  retaining  walls. 
At  the  same  time  there  is  a  shorter  length  of  curved 
work  to  build  than  with  a  semi-circular  form.  The 
cost  of  segmental  culverts  has  been  shown  to  be 
only  about  60%  of  the  cost  of  the  corresponding 
semicircular  ones. 

After  drawing  a  trial  linear  arch  or  line  of  re- 
sistance for  any  particular  case,  the  form  of  this 
trial  curve  will  suggest  the  most  suitable  form  for 
the  intrados  of  the  structure.  For  a  bridge  with 
spandrel  filling  and  loads  increasing  from  the  center 
to  the  springs,  the  elliptical  form  or  a  corresponding 
multi-centered  arch  will  probably  lie  nearest  to  the 
linear  arch,  while  for  an  arch  with  open  spandrels 
the  condition  of  loading  will  be  more  nearly  uni- 
form, and  the  curve  will  be  flatter  at  the  haunches 


PLAIN  CONCRETE  ARC  PI  BRIDGES.  29 

and  approach  the  form  of  parabola.  In  such  cases 
the  segmental  form  would  probably  be  used  instead 
of  the  elliptical.  The  elliptical  form  requires  less 
filling  in  the  haunches  than  the  segmental  arch,  and 
has,  therefore,  less  weight  to  carry.  At  the  same 
time  it  gives  a  greater  amount  of  clearance  under- 
neath, A  semicircular  or  Roman  arch  with  a  large 
rise  generally  requires  the  smallest  piers,  and  in  a 
high  viaduct,  where  the  piers  are  an  important  part 
of  the  total  cost,  this  form  will  be  economical.  The 
exact  line  of  resistance  for  an  arch  under  a  high 
embankment  is  the  geostatic  arch.  It  may,  how- 
ever, be  assumed  as  an  approximate  ellipse.  The 
form  of  the  intrados  under  earth  whose  angle  of 
repose  is  30  degrees  will  then  be  determined  by  the 
equation : — 

Vertical  axis  r- 

Horizontal  axis         A 

In  designing  culvert  arches  it  will  be  advisable  for 
the  engineer  to  consult  standard  plans  for  such 
structures.  Many  considerations  will  appear  that 
might  not  at  first  occur  to  the  designer. 

External  Loads  and  Forces. 

It  has  already  been  shown  that  both  the  amount 
and  direction  of  the  external  forces  acting  on  a 
masonry  arch  are  indefinite.  In  an  arch  supporting 
a  masonry  wall  it  is  usually  assumed  that  the  arch 
carries  the  entire  weight  of  wall  above  it.  This 
is  on  the  side  of  safety,  but  is  certainly  not  correct. 
The  wall  will,  to  a  great  extent,  support  itself. 


30          CONCRETE   BRIDGES   AND   CULVERTS. 

either  acting  as  a  beam  or  arch,  and  the  probability 
is  that  the  weight  of  only  a  small  portion  of  the 
wall  directly  above  the  arch  is  all  that  is  carried 
directly  by  it.  Arches  under  high  embankments 
certainly  do  not  support  the  entire  weight  of  earth 
above  them.  The  earth  corbels  or  arches  itself,  as 
is  plainly  seen  in  the  case  of  a  tunnel,  where  only 
a  small  portion  above  the  crown  is  supported  by 
the  tunnel  center.  It  is  customary  to  consider  that 
arch  bridges  with  spandrel  filling  support  the  entire 
weight  of  such  filling  on  the  arch  ring.  The  fact 
is,  however,  that  the  backing  and  fill  either  arch 
themselves,  to  some  extent,  from  pier  to  pier,  or  if 
the  backing  is  continuous  over  the  pier,  the  backing 
itself  will  then  form  a  cantilever  and  carry  much  of 
the  spandrel  loads. 

The  English  engineer,  Brunei,  many  years  ago 
designed  and  built  a  semi-arch  of  brick,  with  hoop 
iron  bond,  60  feet  in  length,  which  supported  itself 
entirely  by  cantilever  action.  Since  the  introduc- 
tion of  reinforced  concrete  as  a  desirable  material 
for  arch  construction,  it  has  become  common  prac- 
tice to  build  cantilever  arms  or  brackets  on  the 
shore  ends  of  arch  spans,  showing  that  the  canti- 
lever principle  is  just  as  sure  to  come  into  action 
when  continuity  over  the  piers  exists,  as  it  is  that 
the  arch  thrust  itself  is  in  operation.  A  good  illus- 
tration of  this  cantilever  construction  is  shown  in  a 
bridge  recently  built  over  the  Vermillion  River  at 
Wakeman,  Ohio,  and  described  in  Engineering-Con- 
tracting, February  4,  1909.  Somewhat  similar  canti- 


PLAIN  CONCRETE  ARCH  BRIDGES.  31 

lever  arms  were  used  for  retaining  walls  at  the  ends 
of  the  reinforced  concrete  arch  bridge  at  Topeka, 
Kansas. 

Not  only  is  the  amount  of  vertical  loading  from 
the  filling  unknown,  hut  the  horizontal  conjugate 
pressure  on  the  masonry  haunches  is  also  indefinite. 
We  know  that  nearly  all  semicircular  arches,  or 
those  of  similar  form,  after  the  centers  are  removed, 
will  settle  at  the  crown  and  recede  laterally  at  the 
haunches.  The  effect  of  this  settlement  is  to  bring 
conjugate  pressure  on  the  backings,  and,  therefore, 
it  is  certain  that  pressure  exists  there,  but  the 
amount  of  such  pressure  is  unknown.  Semicircular 
arches  require  backing  below  the  point  of  rupture 
to  produce  conjugate  pressure  equal  in  amount  to 
the  crown  thrust.  This  must  be  secured,  either  from 
backing,  fill  or  spandrel  walls.  If  the  point  of  rup- 
ture in  segmental  arches  is  at  or  near  the  skewback, 
the  conjugate  thrust  then  comes  from  the  abutment, 
and  little  or  no  backing  or  corresponding  walls  will 
be  required.  "While  conjugate  pressures  are  neces- 
sary for  stability  below  the  point  of  rupture,  it  has 
been  demonstrated  that  conjugate  tensions  are  nec- 
essary above  that  point,  and  to  secure  that  result, 
rods  have  been  used.  The  intensity  of  conjugate 
thrust  from  earth  filling  with  an  angle  of  repose 
of  30  degrees  is  one-third  of  the  vertical.  It  is  good 
practice  to  cut  the  voussoir  stones  on  the  extrados 
of  the  arch  into  steps  with  horizontal  Lnd  vertical 
faces,  so  the  pressures  on  these  may  be  normal  to 
the  surfaces. 


32          CONCRETE  BRIDGES   AND   CULVERTS. 

Scheffler's  Theorem  assumes  that  all  external 
loading  acts  vertically.  This  is  an  error  on  the  safe 
side  and  will  require  abutments  slightly  heavier 
than  when  conjugate  horizontal  forces  are  consid- 
ered. 

It  has  already  been  stated  that  elliptical  arches 
have  less  fill  or  material  above  them,  and  conse- 
quently less  weight  to  carry,  than  either  segmental 
or  parabolic  arches. 

In  the  case  of  arches  supporting  earth  filling,  the 
form  of  such  filling  will,  to  a  large  extent,  deter- 
mine the  proportion  of  weight  that  bears  upon  the 
arch.  A  long  bridge  will  carry  the  entire  weight 
of  material  above  it,  while  a  culvert  under  a  high 
bank  will  carry  only  a  portion  of  the  material  above 
it.  Sewer  arches  exist  which  would  be  unstable 
without  earth  pressure,  showing  clearly  that  con- 
jugate earth  pressure  does  exist. 

Mathematical  Theory  of  the  Arch. 

The  theory  of  arches  is  very  complex  and  in- 
tricate. Analysts  have  given  much  thought  to  the 
matter,  and  many  volumes  have  been  written,  when 
in  reality,  the  complete  determination  of  the  force 
polygon,  and  the  corresponding  line  of  resistance  in 
the  arch,  constitute  all  the  calculations  involved  in 
the  practical  design  of  a  masonry  arch.  All  methods 
of  computation  are  approximate  only.  The  thick- 
ness of  arch  is  first  assumed  by  comparison  with 
tables  of  existing  arches  or  by  the  use  of  some  em- 
pirical formula.  Lines  of  resistance  are  then  drawn 


PLAIN  CONCRETE  ARCH  BRIDGES.  33 

for  this  arch,  and  if  these  lines  do  not  fall  within 
the  middle  third  of  the  arch  ring,  the  form  is 
changed  and  a  new  line  of  resistance  is  drawn  for 
the  revised  form.  The  calculations  resolve  them- 
selves into  a  series  of  trials.  No  effort  will  be  made 
here  even  to  review  the  many  theories  of  the  arch. 
For  such  investigation  the  student  is  referred  to  the 
writings  of  mathematicians.  Their  conclusions  only 
will  be  given  in  this  book.  The  theory  is  based 
upon  the  assumption  that  joints  will  resist  no  ten- 
sion. 

Stability  Requirements. 

The  requirements  for  complete  stability  in  a  ma- 
sonry arch  are  three  in  number : 

(1)  There  shall  be  no  rotation  of  one  part  of  the 
arch  about  another. 

(2)  There  shall  be  no  sliding  of  one  surface  upon 
another. 

(3)  The  unit  pressure  shall  be  such  that  no  crush- 
ing of  the  arch  material  shall  occur. 

To  insure  the  first  requirement  it  is  necessary 
that  the  line  of  resistance  shall  lie  entirely  within 
the  arch  ring,  and  to  insure  further  that  the  pres- 
sure shall  be  distributed  across  the  entire  section 
of  the  arch,  and  no  tendency  to  opening  of  the  joints 
occur,  it  is  necessary  that  the  line  of  resistance  shall 
lie  within  the  middle  third  of  the  arch  ring.  To 
avoid  sliding  of  one  joint  upon  another,  all  joints, 
including  those  in  the  arch  and  in  the  abutment, 
shall  make  angles  not  less  than  70  degrees  with  the 


34          CONCRETE  BRIDGES  AND   CULVERTS. 

line  of  resistance.  The  friction  coefficient  for  ma- 
sonry joints  is  from  40%  to  50%.  To  avoid  crush- 
ing of  the  arch  material,  the  cross-section  of  the  arch 
shall  be  sufficient,  so  that  the  intensity  of  pressure  at 
the  outer  edge  shall  not  exceed  a  certain  safe  work- 
ing unit.  With  these  three  requirements  fulfilled, 
the  stability  of  the  arch  is  assured.  If  a  line  of 
resistance  cannot  be  drawn  within  the  middle  third 
of  the  arch  ring,  then  it  is  necessary  to  change 
either : — 

(1)  The  thickness  of  the  arch  ring, 

(2)  The  form  of  the  arch,  or 

(3)  The  distribution  of  the  loading. 

Practice  in  the  design  and  construction  of  con- 
crete arches  varies  in  reference  to  the  absence  or 
presence  of  joints  in  the  arch  ring.  In  large  struc- 
tures, where  the  entire  concrete  cannot  be  placed 
from  one  mixing,  it  is  customary  and  sometimes 
necessary  to  provide  joints  in  the  arch  ring,  and  as 
an  additional  precaution  against  sliding  of  such 
joints,  they  may  be  doweled  or  dovetailed  together. 

Ultimate  Values. 

The  ultimate  crushing  values  of  the  common  arch 
materials  are  as  follows : 

Granite    . .  .5,000  to  18,000  pounds  per  square  inch 
Limestone   .4,000  "   16,000       " 
Sandstone  .3,000  "   10,000       " 
Concrete    ..2,000  "     4,000       " 
Brick  300  "        600      " 


PLAIN  CONCRETE  ARCH  BRIDGES.  35 

Working  Units. 

The  working  unit  strength  of  these  materials  at 
the  outer  edge  is  taken  at  one-tenth  of  the  ultimate, 
and  as  the  maximum  pressure  at  the  outer  edge 
when  pressure  at  the  inner  edge  is  zero,  is  twice  the 
mean  or  average  pressure,  this  corresponds  to  using 
a  mean  unit  pressure  of  only  one-twentieth  of  the 
ultimate.  The  necessity  for  this  high  factor  will  be 
seen  from  the  following  considerations.  Experi- 
mental data  on  the  strength  of  masonry  in  bulk  is 
comparatively  small.  Most  experiments  have  been 
made  on  sample  pieces  of  the  material  held  properly 
in  position  with  pressures  applied  normal  to  sur- 
faces. Also  the  crushing  strength  of  masonry  in 
bulk  is  much  less  than  that  of  the  separate  material 
of  which  it  is  composed,  because  of  the  presence  of 
mortar  joints.  On  the  other  hand,  experiments  were 
made  on  sample  cubes  of  material,  while  in  the 
arch  the  material  is  used  in  large  mass,  and  is, 
therefore,  stronger  than  cubes.  Errors  in  workman- 
ship and  in  fitting  of  joints  may  cause  excessive 
pressure  to  occur  on  some  parts  of  joints,  and  little 
or  none  at  all  on  other  parts.  The  entire  system  of 
external  loads  is,  therefore,  uncertain.  Working 
units  may  safely  be  taken  as  follows : 

Granite 500  to  1,500  pounds  per  square  inch 

Limestone    ..-.300  "   1,000       " 
Sandstone  ....200  "      800       " 

Concrete 200  "      500       " 

Brick  .  .80  "      100       "-.         "         "         " 


36          CONCRETE   BRIDGES   AND   CULVERTS. 

A  maximum  pressure  of  400  pounds  per  square 
inch  is  good  practice  for  concrete  arch  rings,  and 
is  suitable  for  a  mixture  of  1-2-4  well  and  carefully 
laid. 

The  above  pressures  refer  to  the  maximum  pres- 
sure at  the  outer  edge  and  not  to  the  mean  or  aver- 
age pressure,  which  would  be  only  one-half  of  the 
above.  These  units  will  give  a  factor  of  safety  of 
ten  in  compression.  The  requirement  that  the  line 
of  resistance  shall  fall  within  the  middle  third  of 
the  joint  produces  a  factor  of  safety  against  rota- 
tion of  three,  and  the  requirement  that  the  angle 
between  the  face  of  joints  and  the  line  of  resistance 
be  not  less  than  70  degrees  produces  a  factor  of 
safety  against  sliding  of  from  one  and  one-half  to 
two. 

Determination  of  Line  of  Resistance. 

Ordinarily,  the  consideration  of  two  cases  of  load- 
ing will  be  sufficient.  (1)  A  uniform  dead  and  live 
load  over  the  entire  structure,  and  (2)  the  entire 
dead  load  with  a  maximum  live  load  over  one-half 
of  the  span  only.  The  absolute  maximum  stresses 
from  partial  loading  may  be  obtained  when  the  live 
load  is  applied  to  somewhat  less  than  one-half  the 
span,  as  .4  to  .45  of  the  length,  but  for  practical 
purposes  it  is  sufficiently  accurate  to  consider  half 
the  span  loaded.  In  certain  cases  it  may  be  neces- 
sary to  consider  the  maximum  dead  load  with  a 
single  concentrated  live  load  at  the  center. 


PLAIN  CONCRETE  ARCH  BRIDGES.  37 

Find  first  the  line  of  resistance  for  the  maximum 
dead  and  live  loads  over  the  entire  structure.  An 
approximate  thickness  will  have  been  assumed  for 
the  arch  ring  at  the  center,  also  the  depth  of  the 
earth  filling  above  as  previously  described,  and  an 
approximate  form  of  arch  will  have  been  selected. 
If  the  bridge  has  spandrel  filling,  the  first  operation 
will  be  to  divide  the  loaded  area  above  the  intrados 
into  a  number  of  vertical  strips,  to  compute  the 
weight  of  material  in  each  of  these  strips  and  the 
live  load  on  them.  In  order  to  simplify  calculations, 
a  portion  of  the  bridge  one  foot  in  length  at  right 
angles  to  the  paper  will  be  considered.  Each  re- 
maining portion  will  be  a  duplicate  of  this.  It  may 
be  necessary  to  draw  a  separate  line  of  resistance 
under  the  side  spandrel  walls,  because  the  weight 
of  wall  masonry  is,  greater  than  earth  fill.  The 
amount  of  conjugate  pressure  of  the  backing  on  the 
haunches  is  then  considered.  For  gravel  and  earth 
the  intensity  of  this  pressure  per  square  foot  or 
other  unit  may  be  taken  at  one-third  of  the  weight 
of  filling  and  live  load  above  the  extrados  at  the 
strip  under  consideration.  Then  the  product  of 
this  horizontal  intensity  and  the  area  of  the  vertical 
projection  of  that  portion  of  the  extrados  under  the 
strip  will  give  the  amount  of  the  conjugate  thrust. 
This  will  be  repeated  for  all  other  strips  and  a 
complete  set  of  loadings  found,  which  should  all  be 
written  in  their  respective  places. 


PLAIN  CONCRETE  ARCH  BRIDGES.  39 

Proceed  next  to  construct  a  force  polygon 
by  drawing  the  various  loadings  to  a  convenient 
scale.  As  arches  are  generally  symmetrical  about 
the  center  and  horizontal  at  that  point,  the  crown 
thrust  for  uniform  loadings  will  likewise  be  hori- 
zontal. The  pole  in  the  force  polygon  will,  there- 
fore, be  on  the  same  horizontal  line  with  the  upper 
end  of  the  first  load  line  at  A.  The  amount  of  this 
crown  thrust  is  unknown,  and  the  pole  distance  can, 
therefore,  be  only  assumed  for  the  present.  Take 
any  pole,  as  that  shown  at  P'  on  Figure  7,  and  draw 
the  corresponding  force  polygon.  Draw  also  the 
corresponding  line  of  resistance  or  funicular  poly- 
gon in  the  arch  ring,  starting  from  any  point  within 
the  middle  third  at  the  crown.  The  resulting  funic- 
ular polygon  is  that  shown  at  ayf.  It  is  evident 
that  the  pole  distance  assumed  was  not  the  correct 
amount  of  the  crown  thrust,  for  the  line  of  resistance 
or  polygon  falls  entirely  outside  of  the  arch  ring. 
Project  the  last  line  of  the  funicular  polygon  till  it 
intersects  the  line  of  crown  pressure  produced  at 
the  point  g.  This  gives  the  position  of  the  resultant 
of  the  assumed  loads,  and  its  direction  will  be  par- 
allel to  the  line  AB  in  the  force  polygon.  The  posi- 
tion of  this  resultant  is  constant,  regardless  of  the 
force  polygon.  Therefore,  the  corresponding  line 
of  any  other  funicular  polygon  produced,  such  as 
that  through  3',  will  likewise  intersect  at  the  same 
point.  Therefore,  through  y  draw  such  a  line,  and 


40         CONCRETE   BRIDGES  AND   CULVERTS. 

from  B  in  the  force  polygon  draw  BP,  intersecting 
the  horizontal  through  A  at  P.  The  distance  AP 
measured  to  the  same  scale  as  the  load  line  will 
represent  the  true  amount  of  the  crown  thrust.  The 
other  lines  radiating  from  P  to  the  various  points 
on  the  load  line  will  truly  represent  the  amount  of 
thrust  at  the  various  points  in  the  arch. 

A  check  on  the  crown  thrust  may  be  made  by 
finding  the  bending  moment  at  the  center  for  all  the 
loads  in  the  same  way  as  for  a  beam,  and  dividing 
this  moment  by  the  rise  of  the  arch.  It  will  be 
remembered,  however,  that  the  rise  is  not  neces- 
sarily the  distance  from  spring  to  crown,  for  in 
flat  arches,  and  especially  in  elliptical  forms,  the 
line  of  resistance  does  not  fall  as  low  as  the  springs. 
The  correct  rise  of  an  arch  is  the  rise  of  the  line  of 
resistance  and  not  the  rise  of  intrados  from  spring 
to  crown. 

It  will  be  seen  by  inspection  that  a  position  of 
the  point  y  was  selected  so  the  line  of  pressure 
would  not  pass  outside  of  the  middle  third  of  the 
arch.  It  approaches  nearest  to  the  limit  under  the 
strip  d.  The  point  opposite  to  this  limiting  position 
is  called  the  point  of  rupture,  and  is  the  point 
at  which  the  arch  first  tends  to  open  at  the  ex- 
trados.  If  the  line  of  resistance  from  the  assumed 
point  3;  had  fallen  outside  the  middle  third  of  the 
arch  ring  at  d,  a  new  point  wrould  then  have  been 
assumed  so  as  to  bring  the  line  of  resistance  en- 


PLAIN  CONCRETE  ARCH  BRIDGES.  41 

tirely  within  the  middle  third  at  the  point  of  rup- 
ture. As  this  point  v  would  approach  very  close 
to  the  middle  third  for  an  arch  of  uniform  thick- 
ness from  crown  to  spring,  the  ring  is  thickened 
at  the  haunch  to  keep  the  line  of  resistance  well 
within  the  middle  third.  The  line  ay,  which  falls 
entirely  within  this  limiting  space,  is,  therefore,  a 
true  line  of  resistance  for  the  maximum  assumed 
dead  and  live  loads.  It  was  necessary  to  determine 
the  crown  thrust  or  pole  distance  by  trial,  because 
there  are  four  unknown  quantities,  the  twTo  vertical 
and  the  two  horizontal  reactions  of  the  arch,  and 
to  determine  these  there  are  only  the  three  equa- 
tions of  equilibrium,  2x=Q,  2y=Q,  2m=Q.  The 
line  BP  applied  at  the  point  3.',  represents  truly  in 
both  direction  and  amount,  the  thrust  of  the  arch 
on  the  abutment.  This  may  be  resolved  into  ver- 
tical and  horizontal  components  as  shown. 

Numerous  ingenious  methods  have  been  adopted 
for  simplifying  the  computations.  For  instance, 
some  writers  prefer  to  construct  what  they  call  a 
reduced  load  contour.  This  consists  in  first  finding 
the  actual  loads  of  arch  ring,  fill,  live  loads,  etc., 
for  each  vertical  strip,  and  reducing  the  height 
above  the  extrados  to  a  corresponding  height,  pro- 
vided the  load  was  caused  entirely  from  stone  or 
material  of  the  same  nature  as  the  arch  ring.  Plot- 
ting these  various  heights  to  scale  above  the  in- 
trados,  and  connecting  the  points  so  found,  pro- 


42          CONCRETE  BRIDGES  AND   CULVERTS. 

duces  a  line  which  is  called  the  reduced  load  con- 
tour. Then  by  making  the  divisions  two  feet  in 
width,  and  scaling  the  length  of  the  two  sides  of 
each  strip,  the  sum  of  the  lengths  scaled  will  repre- 
sent the  area  of  the  enclosed  strip.  Sometimes  the 
areas  are  plotted  on  the  load  line  of  the  force 
polygon  instead  of  the  weights. 

Practice  varies  somewhat  in  reference  to  the 
selecting  of  the  proper  point  in  the  middle  third 
of  the  arch  crown  from  which  to  draw  the  line  of 
resistance.  When  a  hinge  occurs  at  the  crown  there 
is  then  no  uncertainty  as  to  the  correct  position  of 
the  line  of  thrust.  Some  designers  consider  that 
the  position  of  the  line  of  resistance  is  such  as  to 
make  the  crown  thrust  a  minimum  without  causing 
tension  on  any  part  of  the  section.  To  satisfy  these 
conditions,  the  line  would  pass  through  the  upper 
extremity  of  the  middle  third  at  the  crown,  and  at 
the  springs  or  at  the  points  of  rupture,  the  line  of 
resistance  wrould  pass  through  the  inner  extremity 
of  the  middle  third.  Professor  Church  says  that 
the  true  line  of  resistance  is  that  one  corresponding 
most  nearly  with  the  center  line  of  the  arch. 

The  intensity  of  the  unit  pressure  on  a  surface 
may  be  found  from  the  following  formula : — 

W       6Wd 
~~  L  "      L' 

where  p  is  the  maximum  unit  pressure  at  any  part 
of  a  joint,  W  the  total  pressure,  d  the  distance  of 


PLAIN  CONCRETE  ARCH  BRIDGES.  43 

the  center  of  pressure  from  the  center  of  the  arch 
ring,  and  L  the  depth  of  the  arch  ring.  The  formula 
is  general  for  all  positions  of  d,  provided  the  joints 
can  resist  tension.  If  they  cannot  resist  tension, 
the  formula  is  still  general  for  the  values  of  d  up  to 
one-sixth  of  L.  If  d  exceeds  this  amount  the  max- 
imum pressure  is  then  given  by  the  formula : — 

2  W 

P  ''  ~  3  (one  half  L  —  d) 

The  amount  of  crown  thrust  or  pole  distance  may 
be  found  analytically  by  taking  moments  succes- 
sively around  the  various  load  points  in  the  arch. 
The  crown  thrust  will  be  found  a  maximum  when 
moments  are  taken  about  the  load  point  opposite 
to  the  point  of  rupture.  This  is  an  analytical 
method  of  locating  the  point  of  rupture. 

If  the  arch  had  hinges  at  the  crown  and  springs, 
as  are  commonly  built  in  Europe,  the  cro\vn  thrust 
could  then  be  definitely  figured.  The  presence  of 
such  hinges  greatly  facilitates  the  computations  for 
partial  loading,  for  then,  not  only  the  amount  of 
the  crown  thrust,  but  also  its  direction,  are  un- 
known. It  is  no  longer  a  horizontal  thrust. 

The  above  method  of  drawing  a  line  of  resistance 
for  uniform  loads  applied  to  a  pair  of  segmental 
arches  is  illustrated  also  on  the  left  hand  arch  of 
Figure  10. 


44 


CONCRETE  BRIDGES  AND   CULVERTS. 


A  modification  of  the  above  method  of  determin- 
ing the  crown  thrust  and  drawing  the  line  of  re- 
sistance is  shown  in  Figure  8.  The  space  above  the 
arch  ring  is  divided  as  before  into  ten  equal  divi- 
sions and  the  total  load  on  each  calculated  and  indi- 
cated in  the  proper  places.  Beginning  at  the  point 
R,  which  is  the  upper  extremity  of  the  middle  third 
at  the  crown,  the  loads  for  half  the  arch  are  meas- 


Fig.  8 


ured  off  to  scale  on  a  vertical  load  line  Re.  From 
R  and  e  draw  lines  at  45  degrees  with  the  vertical 
intersecting  at  0,  and  from  0  draw  lines  to  the 
points  a,  b,  c  and  d.  Construct  a  polygon  with  sides 
parallel  to  the  lines  Oa,  Ob,  Oc,  Od  and  Oe  and  ex- 
tend the  two  extreme  lines  of  this  polygon  to  their 
intersection  at  D.  Through  D  draw  the  vertical  CE, 


PLAIN  CONCRETE  ARCH  BRIDGES.  45 

intersecting  the  horizontal  line  R  at  C.  The  line  CE 
marks  the  center  of  gravity  of  the  loads  on  the  five 
arch  divisions.  Through  C  draw  the  line  CS  so 
that  the  line  of  resistance,  when  drawn,  will  lie 
within  the  middle  third  of  the  arch  ring.  After 
drawing  the  line  of  resistance,  if  it  should  be  found 
that  any  part  of  it  falls  without  the  middle  third, 
a  new  position  must  then  be  assumed  for  the  point 
S.  Through  e  draw  the  horizontal  line  EF,  inter- 
secting CS  prolonged  at  F.  The  line  FC  will  repre- 
sent truly  to  scale  the  amount  of  the  crown  thrust. 
From  R  lay  off  on  a  horizontal  line  through  R,  the 
distance  RP,  equal  to  FE,  and  join  P  with  the  points 
a,  b,  c,  d  and  e.  From  R  draw  the  line  of  resistance 
with  sides  parallel  to  the  lines  Pa,  Pfr,  etc.  If  any 
part  of  this  line  of  resistance  falls  outside  of  the 
middle  third  of  the  arch  ring,  a  new  position  must 
then  be  assumed  for  the  point  S,  and  another  line 
of  resistance  drawn,  falling  entirely  within  the  mid- 
dle third.  If  no  such  line  of  resistance  can  be 
drawn,  then  either  the  form  of  the  arch  or  its  thick- 
ness must  be  changed  until  a  line  of  resistance  can 
be  drawn  lying  entirely  within  the  middle  third: 

Line  of  Resistance — Partial  Loading. 

Consider  next  the  case   of  a  maximum  live  load 
over    half    the    span,    acting    in    conjunction    with 


PLAIN  CONCRETE  ARCH  BRIDGES.  47 

the  maximum  dead  load.  Both  halves  of  the  arch 
must  then  be  considered.  As  before,  the  portion 
of  the  bridge  above  the  intrados  is  divided  into 
vertical  strips,  and  the  vertical  and  conjugate  load- 
ings written  down  in  their  respective  places.  A 
load  line,  ABC,  is  drawn,  and  any  trial  pole,  P', 
assumed.  With  this  position  of  pole,  the  funicular 
polygon  shown  in  dotted  lines  is  drawn.  By  using 
a  little  care,  the  point  x  may  be  selected,  so  the 
curve  on  the  left  will  fall  within  the  middle  third, 
or  tangent  to  it.  It  will  be  seen  that  this  line  of 
resistance  shown  dotted,  falls  outside  of  the  middle 
third  in  two  places  and  intersects  the  outer  vertical 
through  e'  at  3-.  This  curve  cuts  the  center  line 
of  arch  at  /'.  See  if  it  is  possible  to  draw  another 
line  of  resistance,  so  that  it  will  -cut  the  center  of 
the  span  at  the  point  t  and  pass  through  the  point  y. 
From  P'  draw  a  line  parallel  to  t'  y'  intersecting 
AB  at  D,  and  from  D  drawr  another  line  DP  parallel 
to  ty.  The  new  pole  will  lie  on  the  line  DP.  Also 
through  P'  draw  a  line  parallel  to  xy'  intersecting 
the  load  line  in  Q,  and  from  Q  draw  another  line  QP 
parallel  to  .vy,  intersecting  the  line  DP  at  P.  The 
point  will  be  the  correct  position  of  the  pole,  in 
order  to  have  the  line  of  resistance  pass  through 
the  three  points,  .r,  t  and  y.  The  distance  H  in  the 
force  polygon  may  be  verified  analytically  as  fol- 
lows : — 


PLAIN  CONCRETE  ARCH  BRIDGES.  49 


From  this  equation  the  value  of  H  may  be  found. 
and  the  point  P  will  lie  on  the  line  QP  at  a  distance 
II  from  the  load  line.  The  line  of  resistance  xty  is 
tangent  to  the  line  of  middle  third  in  the  strip  d. 
The  point  where  lines  become  tangent  might  have 
been  taken  as  the  required  point  through  which, 
with  x  and  /,  it  was  desired  to  pass  a  line  of  re- 
sistance. The  corresponding  line  would  have  been 
found  in  a  manner  similar  to  that  described.  It 
will  be  seen  that  the  line  xty  lies  entirely  within 
the  middle  third  of  the  arch,  and  the  arch  as  drawn 
is,  therefore,  stable.  If  it  had  been  found  impossible 
to  draw  a  line  of  resistance  within  the  limits  of  the 
middle  third,  it  would  have  been  necessary  to 
change  either  (1)  the  form  of  the  arch;  (2)  the 
thickness  of  the  arch;  or  (3)  the  distribution  of  the 
arch  loading.  A  similar  method  applied  to  seg- 
mental  arches  is  shown  in  Figure  10.  In  this 
case  the  bridge  was  designed  to  carry  a  double 
line  of  railroad,  with  tracks  15  feet  apart  on 
centers.  It  was  assumed  that  the  ties  and  earth  fill- 
ing distribute  the  weight  of  each  track  and  the  live 
load  thereon  evenly  over  one-half  the  width  of  the 
bridge.  This  assumption  may  not  be  true,  but  it 
is  as  reasonable  an  approximation  as  can  be  made. 
The  live  load  wras  assumed  equal  to  Cooper's  stand- 
ard E  50,  and  for  35-foot  spans  is  equivalent  to  a 
uniform  live  load  of  10,000  pounds  per  lineal  foot, 
which  was  considered  evenly  distributed  over  a 
width  of  15  feet,  amounting  to  667  pounds  per  lineal 


50          CONCRETE   BRIDGES   AND   CULVERTS. 

foot  in  width  of  bridge.  For  partial  loading,  the 
equivalent  uniform  live  load  on  half  the  span  was 
assumed  at  11,500  pounds  per  foot  of  track. 

Point  of  Rupture. 

The  point  of  rupture  is  that  point  of  the  arch 
ring. at  the  haunches  where  the  joints  tend  to  open 
at  the  extrados,  or  where  the  line  of  resistance  lies 
closest  to  the  inner  edge  of  the  arch.  By  some 
writers  this  point  is  considered  the  real  springing 
point  of  the  arch,  and  any  part  of  the  arch  below 
the  point  of  rupture  is  considered  as  part  of  the 
pier  or  abutment.  Its  position  can  best  be  deter- 
mined graphically  when  drawing  the  resistance  line, 
and,  as  far  as  the  arch  itself  is  concerned,  the  line 
of  resistance  is  required  only  above  the  point  of 
rupture.  It  is,  however,  continued  further  for  de- 
termining the  stability  of  the  pier. 

The  following  empirical  rule  gives  approximately 
the  required  thickness  for  circular  segmental  arch 
rings  at  the  point  of  rupture.  In  the  following 
equation  £— crown  thickness,  d=required  thickness 
at  point  of  rupture,  when 

1*1  m^ 

_  >  =  1  then  d=2.00  t 
span 

=  £  then  d=1.40  * 
=  j-  then  d=1.24  t 
=TVthend=1.15* 


In   reference   to   the   necessary   thickness   of  the 
arch  ring  at  various  points  between  the  crown  and 


PLAIN  CONCRETE  ARCH  BRIDGES.  51 


springs,  the  vertical  projection  of  every  section  cut- 
ting the  arch  ring  normal  to  the  line  of  resistance 
must  be  at  least  as  great  as  the  vertical  depth  of 
arch  ring  at  the  crown. 

The  position  of  the  point  of  rupture  generally 
occurs  at  about  that  point  of  the  arch  where  the 
normal  to  the  line  of  pressure  makes  an  angle  of 
45  degrees  with  the  horizontal.  It  may  be  said  that 
it  never  falls  lower  than  an  angle  of  30  degrees 
with  the  horizontal  and  generally  between  35  and 
45  degrees  with  the  horizontal. 

Determination  of  Arch  Thickness. 

The  amount  of  pressure  at  the  various  points  of 
the  arch  have  now  been  determined.  It  will  be  seen 
that  these  pressures  increase  from  crown  to  spring 
in  proportion  to  the  rise  of  the  arch.  In  semi- 
circular arches  the  thrust  at  the  spring  may  be 
three  to  four  times  the  thrust  at  the  crown.  The 
relative  position  of  the  center  of  arch  and  the  line 
of  resistance  must  be  examined  and  suitable  unit 
pressures  selected  for  the  various  points.  If  the 
line  of  resistance  is  at  either  limit  of  the  middle 
third,  the  mean  unit  pressure  will  then  be  one-half 
of  the  maximum  at  the  outer  edge.  This  is  the 
usual  assumption.  Then  the  area  obtained  by 
dividing  the  total  pressures  by  the  working  units 
will  be  the  required  area  of  material  at  various 
points  of  the  arch.  Most  authorities  on  the  subject 
recommend  liberal  sizes,  not  only  because  the  usual 
arch  material  is  not  expensive,  but  also  on  account 


52          CONCRETE   BRIDGES   AND   CULVERTS. 

of  the  uncertainty  of  so  many  conditions  in  connec- 
tion with  the  whole  matter. 

Backing. 

Reference  has  already  been  made  to  the  point  of 
rupture.  It  is  that  point  on  the  extrados  of  the 
arch  where  the  joints  tend  to  open,  and  it  occurs 
opposite  that  point  where  the  line  of  pressure  ap- 
proaches nearest  to  the  intrados.  It  is  known  in 
the  failure  of  flat  arches  that  the  joints  open  at  the 
intrados  of  the  crown,  and  extrados  at  the  two 
points  of  rupture,  and  the  haunches  recede  later- 
ally, allowing  the  central  part  of  the  arch  to  fall. 
In  order  to  resist  and  counteract  this  lateral  move- 
ment of  the  haunches  and  apply  horizontal  conju- 
gate thrust  thereto,  that  part  of  the  extrados  from 
the  point  of  rupture  down  to  the  pier  is  filled  gen- 
erally with  backing  of  rubble  masonry  or  concrete 
laid  in  horizontal  layers.  Semicircular  arches  re- 
quire backing  sufficient  to  produce  conjugate  pres- 
sures equal  to  the  crown  thrust.  Segmental  arches 
which  have  a  horizontal  thrust  component  at  the 
spring  requires  less  backing  than  semicircular  ones. 

Waterproofing  and  Drainage. 

Previous  mention  has  already  been  made  of 
waterproofing.  This  is  necessary  to  prevent  water 
soaking  into  the  joints  and  freezing,  thereby 
tending  to  disintegrate  the  masonry.  A\7aterproof- 
ing  is  necessary  also  'to  prevent  drainage  water  leak- 
ing through  the  arch  and  discoloring  or  otherwise 
disfiguring  the  structure.  To  prevent  such  leakage 


PLAIN  CONCRETE  ARCH  BRIDGES.  53 

it  is  customary  to  cover  the  upper  surface  of  the 
arch  and  backing  with  a  layer  of  bituminous  con- 
crete or  clay  puddle.  Clay  should  contain  enough 
sand  to  prevent  the  clay  from  cracking  when  dry. 
Waterproofing  may  be  accomplished  by  applying  a 
layer  of  rich  mortar  and  surfacing  it  with  neat 
cement,  on  top  of  which  is  poured  a  coating  of  tar, 
pitch  or  asphaltum.  The  upper  surface  of  the  back- 
ing must  have  sufficient  slope  to  carry  drainage 
water  to  the  gutter,  where  it  may  be  discharged 
through  pipes  built  into  either  the  arch  soffit  or  the 
side  spandrel  walls. 

Intermediate  Piers. 

In  making  preliminary  designs  of  piers,  use  may 
be  made  of  empirical  formula  to  determine  approx- 
imate sizes.  Rankine's  rule  is  to  make  the  thick- 
ness of  piers  at  spring  from  one-sixth  to  one-seventh 
of  the  span  or  arch  for  intermediate  piers,  and  one- 
fourth  of  the  span  for  abutment  piers.  Intermediate 
piers  must  be  of  sufficient  area  to  resist  crushing 
from  the  maximum  loads,  and  in  proportioning  the 
base  of  pier  the  weight  of  the  pier  itself  must  be 
added  to  the  imposed  loads.  Intermediate  piers 
must  also  have  sufficient  stability  to  resist  the  over- 
turning effect  of  unbalanced  thrusts  on  the  adjoin- 
ing spans.  Such  unbalanced  thrusts  will  occur  if 
the  adjoining  spans  are  of  different  lengths,  or  if 
one  only,  is  subject  to  live  load.  For  such  condi- 
tions the  center  of  pressure  shall  fall  within  the 
middle  third  of  pier  base.  Piers  must  be  given 


54          CONCRETE   BRIDGES   AND    CULVERTS. 

sufficient  spread  at  the  base,  so  the  pressure  on  the 
foundation  will  not  exceed  a  safe  unit.  To  neutral- 
ize the  effect  of  unequal  thrust  on  the  piers  from 
spans  of  different  lengths,  the  shorter  span  may 
have  a  less  rise  with  a  correspondingly  greater 
amount  of  filling.  This  will  tend  to  produce  a  thrust 
from  the  smaller  span  sufficiently  large  to  equal 
that  from  the  longer  one.  Another  method  is  to 
incline  the  shorter  span  upward  so  the  thrust  will 
act  on  the  pier  at  a  point  somewhat  higher  than  the 
corresponding  thrust  from  the  longer  span.  In 
writing  on  this  subject,  Rankine  says:  "Each  pier 
of  a  series  should  have  sufficient  stability  to  resist 
the  thrust  which  acts  upon  it,  when  one  only  of  the 
arches  which  spring  from  it  is  loaded  with  a  travel- 
ing load.  That  thrust  may  be  roughly  computed  by 
multiplying  the  traveling  load  per  lineal  foot  by  the 
radius  of  curvature  of  the  intrados  at  its  crown  in 
feet."  The  mathematical  investigation  of  piers  is 
shown  in  Figures  7,  9  and  10. 

Abutment  Piers. 

Bridges  having  a  series  of  spans  should  have  abut- 
ment piers  at  intervals  in  order  that  the  possible  fail- 
ure of  one  span  would  not  cause  the  entire  structure 
to  fail.  Abutment  piers  are  useful  also  in  allowing 
false  work  centers  to  be  removed  from  some  of  the 
spans,  without  waiting  for  the  completion  of  the  en- 
tire structure.  When  spring  lines  can  be  located 
close  to  the  foundations,  it  may  be  advantageous  to 
make  all  piers,  abutment  piers.  This  was  the  case 


PLAIN  CONCRETE  ARCH  BRIDGES.  55 

in  the  long  masonry  viaduct  recently  built  at  Santa 
Ana  in  California,  on  the  line  of  the  San  Pedro,  Los 
Angeles  &  Salt  Lake  Railroad.  (See  Engineering 
Record,  September  9,  1905.)  When  it  is  imprac- 
ticable to  make  all  piers  abutment  piers,  it  will  then 
be  well  to  have  every  third  or  fifth  one  of  the  type. 
Such  piers  may  be  designed  with  a  factor  of  safety 
against  overturning  of  from  one  and  one-half  to 
two.  It  will  be  noticed  that  the  point  of  intersec- 
tion of  the  arch  thrust  with  the  load  line  through 
the  center  of  gravity  of  the  piers,  falls  lower  in  the 
abutment  pier  than  in  the  intermediate  ones,. owing 
to  the  greater  width  of  pier.  This  is  an  advantage 
and  will  bring  the  resultant  pressure  nearer  to  the 
center  line  of  the  pier  base.  Trautwine's  approxi- 
mate formula  for  the  thickness  of  abutment  piers 
at  the  springing  is  to  make  the  thickness  equal  to 
one-fifth  of  the  crown  radius  plus  one-tenth  of  the 
rise,  plus  tAvo  feet. 

Abutments. 

In  proportioning  abutment  piers,  it  is  not  neces- 
sary to  keep  the  resultant  pressure  within  the  mid- 
dle third  of  the  base,  if  the  maximum  pressure  at 
the  outer  edge  does  not  exceed  the  allowable  unit 
pressure.  Trautwine's  empirical  rule  for  the  thick- 
ness of  abutments  at  the  springs  is  the  same  as  was 
given  above  for  abutment  piers.  This  approximate 
size  will  assist  in  establishing  the  correct  or  final 
one  and  the  rule  gives  a  thickness  intended  to  be 
sufficient  without  depending  upon  the  existence  of 


56          CONCRETE   BRIDGES   AND   CUU7ERTS. 

earth  pressure  from  behind.  Abutments  sustaining 
high  banks  of  loose  material,  must  be  proportioned, 
not  only  for  the  arch  thrust,  but  also  as  retaining 
walls. 

There  is  frequently  more  masonry  in  the  abut- 
ments of  a  bridge  than  in  the  span  itself.  For  this 
reason  it  is  desirable  to  consider  carefully  any  op- 
portunities for  saving  material  in  the  abutments. 
Placing  the  arch  spring  down  near  the  ground, 
greatly  reduces  the  overturning  moment  on  the 
abutments  and  causes  a  considerable  saving  of  ma- 
terial. In  bridges  with  several  arch  spans,  even 
though  the  spring  lines  on  the  piers  must  be  high 
to  secure  a  clearance  underneath  the  bridge,  the 
springs  at  the  end  abutments  may  sometimes  bo 
kept  down  lower  than  the  corresponding  springs  on 
the  pier,  or  if  abutments  must  be  high,  it  may  be 
economical  to  use  ribbed  abutments,  cored  out  aivl 
reinforced  with  metal  bars,  if  necessary. 

The  use  of  pavement  ties  of  either  wood  or  metal, 
will  cause  the  arch  thrusts  to  counteract  each  other, 
and  thereby  greatly  reduce  the  size  of  abutments. 
This  expedient  has  not  been  used  to  any  great  ex- 
tent until  recent  years,  and  even  now  is  used  chiefly 
for  bridges  of  reinforced  concrete. 

A  wide  and  shallow  waterway  is  more  effective 
than  a  narrow  but  higher  one  of  the  same  area.  Fig- 
ure 11  shows  some  possible  abutment  forms.  At 
A  and  C  are  shown  abutments  where  the  concrete 
in  front  of  dotted  line,  not  only  is  of  no  service  or 
benefit,  but  actually  decreases  the  area  of  waterway 


PLAIN  CONCRETE  ARCH  BRIDGES. 


57 


and  at  the  same  time  adds  to  the  cost  of  the  struc- 
ture. It  will  be  seen,  however,  that  the  abutment 
A  is  one  of  the  most  common  forms  used  in  nearly 


ARCH    ABUTMENTS. 

all  old  arch  bridges.  If  for  any  sufficient  reason, 
vertical  sides  are  desirable  or  necessary,  it  will  be 
economy  to  build  independent  side  walls,  as  shown 


58          CONCRETE   BRIDGES   AND   CULVERTS. 

at  B,   rather  than   waste   material   by   making  the 
whole  abutment  solid. 

At  E  are  shown  old  and  new  methods  of  construc- 
tion. The  dotted  lines  showing  an  abutment  built 
on  level  foundation  is  the  method  given  by  Traut- 
wine  and  the  one  generally  used  until  recent  years. 
It  will  be  seen,  however,  that  the  forms  shown  at  E 
in  full  lines  is  equally  effective  in  transmitting 
thrusts  to  the  soil,  and  requires  somewhat  less  ma- 
terial. If  vertical  sides  are  not  required,  some  ad- 
ditional material  may  be  saved  by  using  the  method 
shown  by  dotted  line  at  C.  D  is  suitable  for  arches 
with  considerable  rise  on  hard  soil  or  loose  rock, 
and  F  shows  a  form  of  abutment  in  which  the  arch 
thrusts  against  solid  rock. 

In  designing  abutments,  it  is  safer  to  discard  tho 
effect  of  conjugate  earth  pressure  on  the  arch  ex- 
trados.  The  abutments  will  then  be  somewhat 
heavier,  but  the  error  wTill  be  on  the  side  of  safety. 
Rankine  says  that  the  thickness  of  abutments  is 
often  from  one-third  to  one-fifth  of  the  radius  of 
curvature  at  the  crown.  Flaring  wing  walls,  25  feet 
in  height  or  less,  rigidly  connected  to  the  abutment 
face,  will  ordinarily  be  safe  with  a  base  equal  in 
width  to  one-fifth  of  the  height.  This  is  only  half 
the  thickness  usually  given  to  retaining  walls,  and 
is  less  because  of  the  angular  connection  to  the 
abutment  face. 

Foundations. 

Piers  and  abutments  must  have  sufficient  spread 
at  the  base,  so  the  load  on  the  foundation  will  not 


PLAIN  CONCRETE  ARCH  BRIDGES.  59 

exceed  a  safe  unit.  For  soil,  this  will  not  ordinarily 
exceed  from  two  to  four  tons  per  square  foot  at  the 
outer  edge  of  the  pier,  where  pressure  is  the  great- 
est. If  piles  are  used,  the  same  precaution  will  be 
taken.  Sloping  piles  have  occasionally  been  used 
in  arch  foundations  for  resisting  the  arch  thrust, 
but  they  are  more  difficult  to  drive  than  plumb 
piles.  The  Jamestown  Exposition  bridge,  Figure 
28,  has  26  plumb  and  126  batter  piles  under  each 
abutment.  The  maximum  allowable  load  on  piles 
should  not  exceed  from  15  to  25  tons  each,  depend- 
ing upon  the  penetration  of  the  pile  at  the  last  blow 
of  the  hammer.  Allowance  must  be  made  for  the 
resultant  pressure  on  the  base  falling  outside  of  the 
center.  It  need  not  necessarily  be  confined  to  the 
middle  third,  provided  the  pressure  on  the  founda- 
tions at  the  outer  edge  is  not  excessive. 

In  his  treatise  on  Masonry  Construction,  Profes- 
sor Baker  gives  the  following  values  for  safe  bear- 
ing power  of  soils : 

Tons  per 
square  foot. 

Rock  equal  to  best  ashlar 25  to  30 

Rock  equal  to  best  brick  masonry 15  to  20 

Rock  equal  to  poor  brick  masonry 5  to  10 

Clay,  dry  thick  beds 4  to     6 

Clay — moderately  dry  thick  beds 2  to     4 

Clay—soft    1  to     2 

Gravel  and  coarse  sand  well  cemented 8  to  10 

Sand — compact  and  well  cemented 4  to     6 

Sand — clean  and  dry 2  to     4 

Quicksand,  alluvial  soil,  etc !/2  to     1 


60          CONCRETE   BRIDGES   AND   CULVERTS. 

Expansion. 

It  is  well  to  provide  for  possible  expansion,  so 
cracks  will  not  appear  in  the  finished  surface.  In 
tho  case  of  the  Connecticut  Avenue  Bridge  at  Wash- 
ington, shown  on  page  88,  one-half  inch  expansion 
joints  are  provided  throughout  the  entire  height  of 
the  spandrels,  from  spring  to  the  floor  over  the  piers 
and  across  the  roadway.  These  arches  are  150  feet 
in  length  and  semicircular.  After  the  completion 
of  the  concrete  arch  bridge  over  Big  Muddy  River 
on  the  Illinois  Central  Railroad  (See  Engineering 
News,  November  12,  1903)  an  examination  was 
made  during  a  period  of  several  months,  and  almost 
no  expansion  whatever  was  discovered. 

Surface  Finish. 

Various  methods  have  been  adopted  for  procuring 
satisfactory  surface  finish  on  concrete  structures. 
Among  these  methods  may  be  mentioned  cement 
washing,  tooling,  sand  blasting,  rough  casting  or 
slap  dashing,  scrubbing,  cold-water  painting^  and 
acid  treating.  The  Connecticut  Avenue  Bridge  at 
"Washington  has  corners  and  moldings  made  of  con- 
crete blocks,  and  to  remove  form  marks  the  body 
and  flat  face  work  were  bush  hammered. 

The  Walnut  Lane  Bridge  at  Philadelphia  has  a 
rough  surface  finish  similar  to  pebble  dash,  but  of 
coarser  grain.  The  surface  shows  stone  chips  not 
larger  than  three-eighths  of  an  inch  in  diameter, 
formed  by  washing  the  concrete  face  before  the  ce- 
ment had  hardened.  A  more  expensive  method  of 


PLAIN  CONCRETE  ARCH  BRIDGES.  61 

securing  a  finished  surface  is  to  build  all  exposed 
surfaces  of  cut-stone  work,  or  a  combination  of 
stone  and  brick,  using  concrete  for  the  body  of  the 
work  only.  The  Green  Island  Concrete  Bridge  at 
Niagara  Trails  has  surfacing  on  the  spandrels  and 
piers  of  cut  stone,  and  other  bridges  have  been  simi- 
larly built  at  Indianapolis  and  elsewhere.  Many 
bridges  generally  known  as  stone  masonry  bridges 
are  stone  only  on  the  surface,  with  the  body  of  pie^s, 
arches  and  backing  composed  entirely  of  co^c^ete. 
The  Rockville  stone  arch  bridge  built  by  the  Penn- 
sylvania Railroad  Company  over  the  Susquehanna 
River  is  of  this  construction.  It  has  stone  facing 
throughout,  including  the  soffits,  spandrels  and 
piers.  In  building  an  ornamental  concrete  foot 
bridge  over  two  lines  of  railroad  at  Como  Park,  St. 
Paul,  to  avoid  the  appearance  of  form  marking  on 
the  finished  surface  of  the  bridge,  the  entire  surface 
of  the  lagging  and  moulds  was  lathed  and  finished 
with  fine  plaster.  In  the  National  Zoological  Park, 
Washington,  is  a  concrete  bridge  faced  on  the  span- 
drels and  parapets  with  natural  boulders,  which  ex- 
tend down  six  inches  or  more  below  the  concrete 
soffit.  In  San  Francisco  are  several  concrete  bridges 
with  rustic  surface  finish,  made  to  represent  natural 
boulders,  but  really  formed  of  moulded  concrete. 
These  boulder  and  rustic  surfaces  are  appropriate 
for  certain  wooded  parks  or  rural  places,  but  are  not 
suitable  for  general  adoption. 

Engineering-Contracting  for  January  6, 1909,  con- 
tains illustrations  of  concrete  surface  effects  secured 


PLAIN  CONCRETE  ARCH  BRIDGES.  63 

by  various  methods  on  laboratory  samples.  It  will 
be  understood,  however,  that  better  results  would 
be  obtained  under  these  conditions  than  could  be  ex- 
pected on  larger  surfaces  where  one  of  its  chief  diffi- 
culties is  to  produce  uniform  effects. 

Stony  Brook  Bridge  in  the  Boston  Fenways  has 
granite  trimmings  with  spreckled  brick  facing,  while 
the  arch  soffits  are  lined  with  glazed  brick  of  vary- 
ing patterns  and  colors. 

There  is  a  very  artistic  three-span  arch  bridge 
over  the  river  at  Des  Moines,  Iowa,  that  has  vitrified 
brick  facing.  The  spans  are  each  100  feet  in  length 
and  elliptical  in  form.  The  brick  facing  with  trim- 
mings of  a  lighter  color  presents  a  very  pleasing 
appearance. 

Another  method  of  preventing  form  marks  from 
appearing  on  the  concrete  surface  is  to  cover  the 
lagging  with  a  layer  of  fine  clay  and  overlay  the 
same  with  building  paper. 

Cost  of  Concrete  Arch  Bridges. 

The  cost  of  concrete  bridges  varies  with  local  re- 
quirements and  conditions.  The  following  original 
formula  gives  the  cost  of  solid  concrete  arch  bridges 
for  both  railroads  and  highways.  The  formula  is 

0  ==«=*' 


100 

where  C  is  the  cost  in  dollars  per  square  foot  of  road- 
way, H  the  general  height  of  the  bridge  at  the  center, 
W  the  total  width  and  F  a  variable  factor  given  by 
the  following  table: 


64          CONCRETE   BRIDGES   AND   CULVERTS. 

200,  then  F  is  1.5 

"  1.0 

"  .65 

"  .48 

"  .42 

"  .JIG 

"  .32 

"'  .285 

"  .202  and .  F'  is  .00 

'•  .224     "     "      .95 

"'  .20       <•     "      .04 

':  .18       "     "      .03 

••  .104     "     "      .02 

••  .152     "      "      .01 

«  .141      "     "      .88 

"  .133     "     "      .80 

'*  .125      "      '•      .85 

"  .110      "      "      .82 

«  .113     "     "      .80 

As  the  height  of  the  bridge  multiplied  by  its  width 
gives  the  cross  sectional  area,  the  function  HW  may 
be  represented  by  the  letter  A.  Factors  F  refer  to 
arch  bridges  with  complete  soffit  slabs,  while  factors 
F'  refer  to  arch  bridges  with  partial  soffit  slabs,  such 
as  used  in  the  Walnut  Lane  bridge  in  Philadelphia, 
and  the  Detroit  Ave.  bridge  in  Cleveland. 

The  cost  of  concrete  bridges  is  affected  more  by 
natural  conditions  and  the  selection  of  the  economic 
forms  than  by  the  live  load  to  which  these  bridges 


When 

A  is   200, 

ft 

500, 

Cf 

1000, 

(  ( 

"   1500, 

t  ( 

"   2000, 

i  ( 

"   2500, 

" 

3000, 

a 

"   3500, 

te 

"   4000, 

-  t  i 

"   5000, 

(( 

0000. 

K 

"   7000. 

(( 

"   8000, 

(( 

"   0000, 

(  i 

"  10000, 

(( 

"  11000, 

i  t 

"  12000, 

it 

"  13000, 

a 

"  14000, 

PLAIN  CONCRETE  ARCH  BRIDGES.  65 

are  subjected.  This  is  shown  by  the  above  formula 
applying  equally  to  concrete  arch  bridges  for  both 
railroads  and  highways. 

The  weight  of  concrete  and  other  materials  is 
greater  than  the  imposed  live  load  and  the  live  loads 
are  not,  therefore,  the  chief  considerations  in  deter- 
mining the  ultimate  cost. 

The  formula  clearly  shows  that  concrete  arch 
bridges  vary  in  cost  in  proportion  to  the  product  of 
their  weight  and  width.  Bridges  with  a  small  cross 
sectional  area  cost  as  low  a  price  as  $2.50  per  square 
foot  of  floor  surface,  while  large  monumental  bridges 
may  cost  as  high  as  $16.00  per  square  foot. 

The  formula  also  clearly  shows  the  great  economy 
in  using  partial  in  place  of  complete  soffit  slabs,  and 
this  economy  may  be  still  further  increased  by  the 
use  of  ribbed  arch  designs.  Kibbed  arches  are  not, 
however,  generally  suitable  for  construction  in  solid 
concrete  and  the  treatment  of  this  style  of  arch  will 
therefore  be  taken  up  later,  with  the  design  of  arches 
in  reinforced  concrete. 

Table  No.  1,  giving  details  of  concrete  bridges, 
gives  also  the  total  cost  of  these  structures. 

Design  for  a  Concrete  Arch,  60  Feet  Center  to  Cen- 
ter of  Intermediate  Piers.     Clear  Span  53 
Feet.     Rise  10  Feet. 

The  bridge  consists  of  a  series  of  arches  to  carry 
a  street  over  a  number  of  railroad  tracks.  The  span 
was  arbitrarily  fixed  at  60  feet  center  to  center  of 
intermediate  piers,  or  53  feet  in  the  clear.  This 
provides  clearance  for  four  lines  of  tracks,  13  feet 


66          CONCRETE   BRIDGES   AND   CULVERTS. 

apart  on  centers.  For  a  low  structure  of  this  height, 
shorter  spans  might  have  been  more  economical,  but 
this  length  was  selected  that  the  clearance  way  for 
the  tracks  would  not  be  too  greatly  obstructed  with 
piers.  The  headroom  underneath  is  shown  on  Fig- 
ure 7,  and  is  the  height  generally  required  by  rail- 
road specifications,  being  21  feet  from  the  top  of  rail 
in  the  center  of  track  nearest  to  the  pier.  The 
elliptical  form  was  selected  for  the  reason  that,  with 
the  given  clearance,  it  allows  the  springing  line  to 
fall  lower  than  any  other  form  and  in  this  case  is 
15  feet  above  the  ground.  As  the  viaduct  is  a  long 
one,  it  was  desirable  to  keep  the  entire  height  and 
the  corresponding  cost  down  to  the  lowest  possible 
amount.  A  minimum  rise  of  one-fifth  the  spaa 
was  therefore  selected,  amounting  to  10  feet  from 
spring  to  crown.  The  rise  is  the  semi-minor  axis  of 
the  ellipse  and  not  the  effective  rise  of  the  line  of 
pressure,  which  is  used  later  in  determining  the 
crown  thrust  and  pier  reactions.  The  approximate 
rule  for  the  thickness  of  intermediate  piers  is  to 
make  the  thickness  of  such  piers  one-sixth  to  one- 
seventh  of  the  length  of  span.  This  would  produce 
a  thickness  of  pier  from  7  to  8  feet  at  the  spring  and 
7  feet  was  selected  for  a  trial.  To  determine  an 
approximate  crown  thickness,  Rankine's  rule  was 
used.  For  a  series  of  arches,  it  is  -\r  ^  Radius. 
This  requires  that  the  radius  be  known.  Lay  out  an 
ellipse  graphically  by  the  method  of  five  centers, 
and  the  radius  is  found  to  be  72  feet.  Eankine's 


PLAIN  CONCRETE  ARCH  BRIDGES.  67 

rule,  as  above,  gives  a  thickness  of  3.5,  while  Traut- 
wine's  rule  for  the  approximate  thickness  is  given 
in  his  book,  page  617,  and  is  2.2  feet.  Try  a  thick- 
ness of  2.5  feet.  The  grading  of  the  bridge  up  to  a 
higher  level  in  order  to  secure  a  greater  rise  for  the 
arch  was  considered,  but  as  this  increased  the  quan- 
tities of  material  in  the  superstructure,  and  would 
effect  a  saving  only  in  the  abutment  piers,  the  pl»?i 
was  not  adopted.  A  thickness  of  crown  filling  of 
2.5  feet  was  assumed  from  the  extrados  of  the  arch 
to  the  pavement  surface. 

The  entire  portion  of  the  bridge  above  the  intra- 
dos  was  then  divided  into  strips,  and  the  weight 
for  each  of  these  strips  calculated,  on  the  assump- 
tion that  earth  filling  weighs  100  pounds  per  cubic 
foot,  and  masonry  160  pounds  per  cubic  foot.  A  live 
load  of  150  pounds  per  square  foot  was  assumed  on 
the  roadway.  The  weight  was  computed  for  each 
strip  and  noted  on  Figure  7  in  their  respective 
places.  The  amount  of  conjugate  thrust  was  then 
found  by  taking  the  intensity  of  such  thrust  at  one- 
third  the  weight  of  earth  and  live  load  above  it. 
These  were  also  noted  in  their  proper  places.  Center 
lines  were  then  drawn  through  each  strip,  and  a 
load  diagram  constructed  by  drawing  in  order  the 
various  vertical  and  horizontal  loads  from  A  to  B, 
as  shown  in  Figure  7.  A  trial  pole  P'  was  selected 
and  lines  drawn  connecting  each  of  the  load  points 
on  aB  with  P'.  The  corresponding  funicular  poly- 


68          CONCRETE   BRIDGES   AND   CULVERTS. 

gon  ay  was  drawn  with  lines  parallel  to  the  lines  in 
the  force  polygon  AP',  BP',  etc.  This  is  evidently 
not  the  correct  position  of  the  pole,  for  the  result- 
ing funicular  polygon  lies  almost  entirely  outside 
of  the  arch.  By  prolonging  the  last  string  of  the 
funicular  polygon  to  its  intersection  at  g  with  the 
horizontal  through  the  arch  center  from  a,  we  find 
the  point  of  application  of  the  resultant  of  all  the 
imposed  loads,  which  is  at  g.  The  direction  of  the 
resultant  pressure  would  be  parallel  to  AB.  As  the 
position  of  this  point  is  constant  for  any  other  posi- 
tion of  pole,  we  may  draw  through  y  a  line  yg.  This 
will  represent  the  direction  of  the  actual  pressure 
of  the  arch  on  the  abutment.  Through  B  in  the 
force  polygon  draw  a  line  parallel  to  yg  intersecting 
the  horizontal  through  A  at  P.  The  point  P  will  be 
the  correct  position  of  the  pole,  and  the  distance  AP 
measured  to  the  same  scale  as  the  line  AB,  will  rep- 
resent truly  the  amount  of  the  crown  thrust.  In 
this  case  it  is  42,000  pounds.  This  investigation  is 
for  a  portion  of  the  bridge  one  .foot  in  length  at 
right  angles  to  the  diagram.  Pressures  at  the  var- 
ious points  in  the  arch  correspond  to  the  lengths  of 
lines  in  the  force  polygon.  At  the  pier  for  full 
loading,  the  pressure  is  48,000  pounds. 

Uneven  Loading. 

Lines  of  resistance  were  next  drawn  for  unsym- 
metrical  loading  as  shown  in  Figure  9.  This  has 
already  been  quite  fully  described  under  the  head 
of  Partial  Loads. 


PLAIN  CONCRETE  ARCH  BRIDGES.  69 

Required  Area  in  Arch. 

Using  a  maximum  pressure  of  400  pounds  per 
square  inch  as  a  safe  working  unit  on  concrete  at 
the  outer  edge,  or  200  pounds  per  square  inch  mean 

42000 
pressure,  the  required  area  in    the    arch    is 

200 

or  210  square  inches.  This  requires  a  depth  of  arch 
of  18  inches.  We  have  already  assumed  a  depth  of 
30  inches  so  the  arch  is  secure  against  crushing. 
With  a  depth  of  30  inches,  the  mean  pressure  on  the 
concrete  is  only  116  pounds  per  square  inch,  instead 
of  the  200  pounds  which  is  proposed. 

Intermediate  Piers. 

First  figure  the  required  size  of  pier  to  sustain  the 
total  load  in  compression.  The  total  weight  from 
the  arches  and  the  live  load  is  54,000  pounds.  As- 
sume the  material  of  the  pier  to  be  concrete,  with  an 
allowable  unit  pressure  on  the  outer  edge  of  400 
pounds  per  square  inch.  For  a  mean  working  pres- 
sure assume  half  of  this  amount,  or  200  pounds  per 
square  inch.  The  required  area  in  the  pier  at  spring- 
ing to  sustain  direct  loads  is  therefore  or 

200 

270  square  inches.  As  the  assumed  width  of  pier  at 
the  top  was  7  feet,  the  case  of  full  uniform  loading 
is  evidently  not  the  governing  consideration. 

Consider  next  the  case  of  equal  spans  thrusting  on 
the  pier,  one  with  full  dead  and  live  load  and  the 
other  with  dead  load  only.  The  thrusts  in  these 


70          CONCRETE   BRIDGES   AND   CULVERTS. 

two  cases  are  48,000  and  42,000  pounds  respectively. 

The  total  load  on  the  pier  at  the  level  of  the  ground 

is  therefore  as  follows : — 

Pounds. 

From  fully  loaded  span 26,000 

From  partly  loaded  span 23,000 

Weight  of  pier  .18.000 


Total    67,000 

By  combining  this  load  with  the  arch  thrust,  we 
find  the  resultant  pressure,  the  line  of  which  inter- 
sects the  base  at  ground  level  one  foot  from  the  cen- 
ter of  the  pier,  which  is  well  within  the  middle 
third.  This  result  may  very  easily  be  checked  ana- 
lytically. The  width  of  pier  at  base  is  14  feet,  which 
was  found  as  follows  :— 

The  total  pressure  on  the  soil  is  : — 

Pounds. 

From  bridge 54.000 

From  pier  27,000 


Total   81,000 

Allowing   a   mean   pressure   of   6,000   pounds   per 

square  foot  on  the  soil,  the  required  width  of  pier  is 

8 1000 

or  13.5  feet.     If  the  soil  will  not  sustain 
GOOO 

6,000  pounds  per  square  foot,  which,  allowing  for 
uneven  pressure,  equals  4  to  5  tons  per  square  foot 
at  the  outer  edge,  piles  will  then  be  required. 

Abutment  Piers. 

In  proportioning  the  abutment  pier,  stability  is 
the  chief  consideration.     It  must  be  stable  against 


PLAIN  CONCRETE  ARCH  BRIDGES.  71 

the  thrust  of  arch  from  one  side  only.  This  arch 
thrust  intersects  the  center  of  -the  pier  at  a  distance 
of  14  feet  above  the  ground.  The  overturning 
moment  from  this  thrust  is  therefore  33000 X14,  foot 
pounds.  Using  a  factor  of  one  and  one-half  against 
overturning,  the  necessary  moment  of  stability  is 
33,OOOX14Xli/>,  or  69,300  foot  pounds.  Next  pro- 
ceed to  find  the  half  width  of  pier  base  at  ground 
level.  Calling  this  half  width  A%  the  required  mo- 
ment of  stability  in  foot  pounds  is 
230000? +(2o;X22Xl60)a;  =  69,300  foot  pounds.  In 
the  above,  22  is  the  total  height  of  the  pier  from 
the  top  of  the  ground  to  the  top  of  the  backing,  and 
160  is  the  weight  of  the  pier  material  per  cubic  foot. 
From  the  above  we  obtain  a  quadratic  equation,  and 
solving,  we  find  the  value  of  x  to  be  8.45  feet. 
This  would  be  for  a  pier  writh  vertical  sides.  For 
sloping  sides,  take  a  half  width  at  the  base  of  9 
feet,  as  shown  in  Figure  9.  This  size  of  pier  is 
then  amply  stable  against  overturning. 

Coring  out  the  haunches  by  means  of  interior 
spandrel  walls,  would  evidently  be  no  economy  in 
so  flat  an  arch.  The  cost  of  such  walls  and  arching 
would  be  greater  than  the  saving  in  the  arch  ring 
from  the  reduced  dead  load  and  the  less  amount  of 
filling. 

Illustrations  of  Concrete  and  Masonry  Bridges. 

The  foregoing  table  gives  a  list  of  arch  bridges, 
the  main  arches  of  which  are  built  of  solid  concrete 


72          CONCRETE  BRIDGES   AND   CULVERTS. 

without  metal  reinforcement.  In  one  of  these,  how- 
ever— the  railroad  bridge  over  the  Vermillion  River 
at  Danville — reinforcement  was  actually  used  in  the 
main  arch,  but  was  adopted  only  for  the  purpose  of 
better  uniting  the  concrete  and  preventing  cracks 
from  change  of  temperature.  In  several  of  the 
other  bridges,  noted  in  the  table,  metal  reinforce- 
ment was  used  in  spandrel  arches,  or  other  minor 
parts,  but  as  already  stated,  the  main  arches  have 
been  designed  with  no  provision  for  tension  in  any 
part  of  the  arch  section,  and  consequently  no  need 
for  reinforcing  metal  to  resist  direct  stresses. 

The  table  is  not  intended  to  be  comprehensive  or 
complete,  but  gives  some  details  of  a  few  of  the 
largest  concrete  spans,  the  main  arches  of  which 
are  designed  without  reinforcement.  In  reference 
to  the  Hudson  Memorial  Bridge,  noted  in  this  table, 
and  illustrated  on  page  77,  the  design  calls  for  a 
large  amount  of  metal  reinforcement,  not  for  the 
purpose  of  resisting  any  tensile  stresses  in  the  arch, 
but  rather  to  supplement  the  concrete  in  resisting 
direct  compression.  This  is  a  new  principle  in  arch 
construction,  not  previously  used. 

Illustrations  and  descriptions  of  two  old  Roman 
bridges  are  also  given  for  the  purpose  of  calling 
attention  to  the  superiority  and  permanence  of  ma- 
sonry bridges  over  those  of  any  other  known  type 
or  material.  They  have  existed  for  centuries,  and 
such  bridges  should  endure  after  metal  bridges  have 
disappeared. 


a  8 


74          CONCRETE  BRIDGES  AND   CULVERTS. 
Ponte  Rotto,  Rome. 

As  it  stands  to-day,  this  old  bridge  has  three  stone 
arch  spans,  and  a  suspension  bridge,  spanning  the 
gap  where  other  arches  originally  stood.  The  pres- 
ent bridge  stands  on  the  site  of  the  old  Pons  Aemil- 
iiis,  built  B.  C.  178-142,  which  was  the  first  stone 
bridge  over  the  Tiber  at  Rome.  The  three  remain- 
ing arches  date  from  Julius  ITT,  and  are  richly  orna- 
mented. Two  arches  were  carried  away  by  a  flood 
in  1598,  and  have  never  been  replaced.  The  bridge 
seems  to  be  unfortunately  located,  as  it  has  been 
carried  away  at  least  four  times,  the  first  time  in  A. 
D.  280.  It  was  erected  by  Cains  Flavius,  and  is 
probably  the  first  appearance  of  the  arch  in  bridge 
construction.  It  has  semicircular  arches  and  a 
level  roadway.  The  two  end  arches  were  shorter 
than  the  three  intermediate  ones.  It  is  called  also 
Pons  Palatinus,  Senators'  Bridge,  and  Pons  Lapi- 
deus.  The  bridge  is  similar  in  construction  to  the 
other  old  stone  bridges  of  Rome,  and  is  built  of 
peperino  and  tufa,  faced  with  blocks  of  travertine 
anchored  into  the  body  of  the  masonry.  It  will  bo 
seen  from  the  illustration  that  the  spandrels  and 
parapets  are  highly  ornamented  with  carved  panel 
work  and  each  of  the  piers  above  the  arches  and 
foundations  are  penetrated  with  smaller  arch  open- 
ings. The  panel  work  has  disappeared  fromlhe  left 
shore  span  and  plainly  reveals  the  plan  of  construc- 
tion. It  will  be  seen  that  the  arch  ring  is  built  of 


76 


76         CONCRETE  BRIDGES   AND   CULVERTS. 

different  material  and  differently  laid  than  the 
filling  above  it,  and  that  numerous  openings  occur 
in  the  backing  which  were  doubtless  used  for  the 
purpose  of  anchoring  the  ornamental  facing  to  the 
body  of  the  structure.  It  is  well  known  that,  in  the 
construction  of  bridges  and  aqueducts  built  by  tho 
Romans  and  others-in  early  times,  a  large  amount  of 
concrete  was  used. 

Bridge  of  Augustus  at  Rimini. 

The  old  Roman  bridge  crossing  the  River  Mara- 
chia  at  Rimini,  is  supposed  to  have  been  built  during 
the  reign  of  Emperor  Augustus,  about  14  A.  D.  It 
has  five  arch  spans,  with  very  heavy  piers.  The  de- 
tails that  still  remain  show  that  originally  the 
bridge  was  very  ornamental.  There  are  niches  at 
the  piers,  and  the  heavy'  stone  cornice  is  carried 
on  numerous  brackets.  The  arches  are  all  semi- 
circular, the  end  ones  having  a  span  of  23  feet, 
while  the  three  intermediate  ones  have  spans  of  28 
feet. 

Henry  Hudson  Memorial  Bridge. 

(Reinforced  Concrete  Design.) 

It  is  proposed  to  erect  on  an  extension  of  River- 
side Drive  in  the  City  of  New  York,  a  Memorial 
bridge  over  Spuyten  Duyvil  Creek,  to  commemorate 
the  explorations  and  discoveries  of  Henry  Hudson. 
The  design  accepted  by  the  Municipal  Art  Commis- 


78          COXCRETE  BRIDGES  AND   CULVERTS. 

sion  of  the  City  of  New  York  is  herewith  shown. 
Previous  designs  showing  the  principal  span  framed 
in  steel  were  rejected  as  being  inappropriate  for  a 
great  memorial  bridge.  There  will  be  one  span 
with  a  clear  length  of  703  feet,  and  seven  other 
semicircular  arch  spans  with  clear  lengths  of  108 
feet.  The  total  length  of  the  structure  will  be  2,840 
feet.  The  main  arch  span  will  have  a  rise  of  177 
feet,  and  will  contain  a  large  amount  of  steel,  used, 
not  as  concrete  reinforcement  ordinarily  is,  to  re- 
sist tensile  stresses,  but  rather  to  assist  in  resisting 
the  compressive  stresses  in  the  concrete,  and  there- 
by reduce  the  amount  of  masonry.  The  arch  will 
have  a  crown  thickness  of  15  feet.  There  will  be 
two  decks,  the  upper  one  carrying  a  CO-foot  road- 
way and  two  15-foot  sidewalks,  while  the  lower  deck 
will  be  70  feet  in  width,  and  will  carry  four  lines 
of  electric  railway.  It  is  the  intention  to  omit  the 
construction  of  the  lower  deck  at  the  present  time. 
The  design  provides  for  a  clear  headroom  of  183 
feet  under  the  main  arch.  The  main  piers  will  be 
180  feet  in  width.  The  estimated  cost  is  $3,800,000. 
The  illustration  shows  the  bridge  as  it  will 
appear  to  an  observer  looking  out  over  the  Hudson 
River,  with  the  Palisades  in  the  distance.  The  de- 
sign was  made  by  the  bridge  department  of  the  City 
of  New  York,  at  which  time  C.  M.  Ingersoll  was 
Chief  Engineer,  L.  S.  Moisseiff  Engineer  in  Charge, 
Wm.  H.  Burr,  Consulting  Engineer,  and  Whitney 


PLAIN  CONCRETE  .ARCH  BRIDGES.  79 

Warren,     Architect.     The     next     longest     masonry 
arches  of  the  world  are  as  follows : 

Feet, 
span. 

Stone  arch  bridge  over  Adda  River 230 

Stone  arch  bridge  at  Luxemburg,  Germany 278 

Stone  arch  bridge  at  Plauen,  Germany 295 

Concrete  arch  bridge  at  Gruenwald 230 

Concrete  arch  bridge  at  Walnut  Lane,  Philadel- 
phia     233 

Stein-Teufen  bridge,  Switzerland 259 

Concrete  arch  bridge  at  Rocky  River,  Cleveland. 280 
Aukland,   New  Zealand 320 

Aukland,  New  Zealand,  Bridge. 

A  reinforced  concrete  arch  bridge  is  being  built 
on  the  North  Island,  at  Aukland,  New  Zealand,  with 
a  clear  span  of  320  feet — the  longest  in  existence. 
Several  longer  ones  have  been  projected,  one  over 
the  Mississippi  River  at  Fort  Snelling,  Minn.,  wTith 
two  spans  of  350  feet,  but  none  built.  The  Aukland 
bridge  has,  besides  the  320-foot  center  span,  two  35- 
foot  and  four  70-foot  spans,  with  a  total  length  of 
910  feet.  It  is  40  feet  wide,  and  the  roadway  is  147 
feet  above  the  valley.  The  two  arch  rings  are  hinged 
at  the  springs  and  center.  It  was  commenced  in 
February,  1908,  and  the  contract  calls  for  comple- 
tion in  two  years.  It  adjoins  a  residential  district, 
and  at  one  end  are  the  graves  of  New  Zealand 
pioneers. 


80          CONCRETE   BRIDGES   AND   CULVERTS. 

Monroe  Street  Bridge,  Spokane,  Wash. 

In  the  city  of  Spokane,  Wash.,  plans  are  prepared 
tor  building  a  four-span  concrete  bridge  to  carry 
Monroe  street  at  a  height  of  140  feet  above  the  Spo- 
kane River.  The  main  arch  has  a  clear  span  of  281 
feet,  and  is  divided  into  two  ribs,  16  feet  wide  and 
6  feet  thick  at  the  crown.  It  will  have  open  span- 
drels and  overhanging  sidewalks,  with  Dutch  towers 
at  the  ends  for  public  lavatories.  The  bridge  will 
replace  the  old  steel  cantilever  built  17  years  ago. 
It  will  have  a  50-foot  roadway  and  two  9-foot  side- 
walks, making  a  total  width  of  71  feet  and 
a  total  length  of  791  feet.  The  main  arch 
will  be  segmental  and  the  remaining  ones  semi- 
circular. The  deck  will  be  carried  on  solid  cross 
spandrel  walls,  20  feet  apart.  The  ground  on  the 
north  side  of  the  river  is  naturally  suited  for  an 
arch  bridge,  but  on  the  south  side  the  plan  proposes 
an  abutment  carried  down  to  140  feet  below  street 
level,  consisting  of  four  parallel  walls,  each  4  feet 
in  thickness,  joined  by  numerous  cross  struts  and 
braces.  See  Fig,  16.  J.  C.  "Ralston,  City  Engineer. 
Rocky  River  Bridge,  Cleveland,  Ohio. 

A  concrete  arch  bridge  with  the  longest  masonry 
span  in  America  is  now  being  built  over  Rocky 
River  on  Detroit  avenue,  at  Cleveland,  Ohio.  It  will 
have  a  central  span  of  280  feet  and  five  approach 
spans  of  44  feet  each.  It  will  carry  a  40-foot  road- 
way and  two  sidewalks  8  feet  wide  each.  The  total 
width  over  railings  will  be  GO  feet  and  the  total 
length  708  feet.  The,  main  span  consists  of  two  sep- 


SI 


.7*'  S    a 


III 


84          CONCRETE   BRIDGES   AND   CULVERTS. 

arate  arch  rings  18  feet  wide  at  the  crown,  and 
placed  16  feet  apart.  On  these  arches  the  deck  is 
to  be  carried  on  cross-spandrel  walls.  The  roadway 
level  is  9-4  feet  above  the  surface  of  low  water  and 
the  pavement  will  be  of  brick,  with  two  lines  of 
track  for  heavy  suburban  cars.  Beneath  the  floor 
are  to  be  two  subway  chambers,  3  feet  by  11  feet 
for  the  placing  of  pipes  and  wires.  The  main  arch 
rings  will  contain  no  steel  reinforcement,  as  the  cal- 
culations show  that  no  tension  can  at  any  time  oc- 
cur in  any  part  of  the  arch.  The  sidewalks  project 
out  over  the  face  walls  about  five  feet,  and  are  sup- 
ported on  brackets.  The  entire  structure  will  be 
built  of  concrete.  It  will  be  quite  similar  to  and  47 
feet  longer  than  the  Walnut  Lane  Bridge  at  Phila- 
delphia. The  only  longer  masonry  arch  span  in  ex- 
istence is  the  one  at  Plauen,  in  Germany,  with  a 
span  of  296  feet,  built  of  hard  slate.  Other  pro- 
jected long-span  bridges  are  that  over  the  Neckar 
River  at  Manheim,  with  a  span  of  365  feet,  and  the 
Hudson  Memorial  Bridge  in  New  York  City,  with  a 
span  of  703  feet.  The  Rocky  River  Bridge  was  de- 
signed under  the  direction  of  A.  B.  Lea,  County 
Engineer,  by  A.  M.  Felgate,  Bridge  Engineer.  It  is 
under  construction  by  Schillinger  Brothers,  con- 
tractors of  Chicago.  Wilbur  J.  Watson,  Engineer. 

Walnut  Lane  Bridge,  Philadelphia. 

Walnut  Lane  crosses  the  Wissahickon  valley  on 
a  new  concrete  bridge  at  a  height  of  147  feet  above 
the  river  bed.  At  the  time  of  completion  it  was  the 


to  o 
*J   Q 


86          CONCRETE   BRIDGES   AND   CULVERTS. 

longest  concrete  masonry  bridge,  having  a  clear 
span  of  233  feet.  It  consists  of  two  separate  arch 
rings,  18  feet  wide  at  the  crown,  increasing  to  21 
feet  6  inches  at  the  springs.  At  the  crown  the  two 
rings  are  separated  by  a  space  of  16  feet.  The 
double  rib  construction  is  similar  to  that  used  in 
the  stone  arch  bridge  at  Luxemburg,  Germany,  hav- 
ing a  span  of  275  feet.  The  main  arch  is  an 
approximate  ellipse,  has  a  rise  of  73  feet,  and 
carries  10  cross  wralls  which  support  the  floor 
system.  There  are  also  five  semicircular  approach 
arches  with  clear  spans  of  53  feet.  The  bridge  con- 
nects Germantown  and  Roxborough,  two  residential 
suburbs  of  Philadelphia.  It  has  a  40-foot  roadway, 
and  two  10-foot  sidewalks.  The  entire  structure  is 
solid  concrete,  not  reinforced,  excepting  in  certain 
minor  details.  The  surface  finish  is  rough,  some- 
what similar  to  pebble  dash,  but  of  coarser  grain. 
The  exposed  surface  shows  stone  clips  of  not  over 
three-eighths  inch  in  size,  formed  by  washing  before 
the  cement  had  hardened.  The  total  length  of 
bridge  over  all  is  585  feet,  and  the  cost  $259,000. 
George  S.  AVebster,  Chief  Engineer,  Bureau  of  Sur- 
veys. H.  H.  Quimby,  Bridge  Engineer.  Reilly  & 
Riddle,  Contractors. 

Connecticut  Avenue  Bridge,  Washington. 

Connecticut  Avenue,  one  of  the  chief  thorough- 
fares of  Washington,  is  carried  over  Rock  Creek 
valley  near  its  junction  with  the  Potomac  on  a  new 
concrete  arch  bridge,  about  three  miles  from  the 


lit 


88          CONCRETE   BRIDGES   AND   CULVERTS. 

Capitol  building.  The  roadway  is  120  feet  above 
the  valley  below,  and  is  carried  by  five  semicircu- 
lar arches  of  150-foot  span,  and  two  end  arches  of 
82-foot  span.  It  has  a  35-foot  roadway,  and  two 
sidewalks  8  feet  wide  each,  making  a  total  width  of 
52  feet,  a  clear  length  between  abutments  of  1,068 
feet,  and  a  total  length  of  1,341  feet.  It  wras  com- 
menced in  1889,  and  completed  in  1908.  The  main 
arches  are  hingeless  with -no  reinforcing,  but  the 
spandrel  arches  have  steel  reinforcement.  As  the 
bridge  is  located  in  a  fine  residential  district,  its 
aesthetic  appearance  was  a  matter  of  considerable 
importance.  The  face  rings  of  the  arch,  pier  cor- 
ners, mouldings  and  all  trimmings  below  the  granite 
coping,  are  moulded  concrete  blocks.  The  remaining 
part  of  the  exposed  concrete  surface  is  bush  ham- 
mered, for  the  purpose  of  presenting  a  more  uniform 
and  pleasing  appearance.  The  cost  of  the  falsework 
was  about  $50,000,  but  on  this  there  was  a  salvage 
of  about  $15,000.  The  cost  of  framing  the  false- 
work was  $9  per  thousand  feet  of  lumber.  Moulded 
cement  blocks  cost  $15  per  cubic  yard.  The  total 
cost  of  the  structure  complete  was  $850,000,  equal 
to  $639  per  lineal  foot,  or  $12.30  per  square  foot  of 
floor  surface.  It  is  built  from  a  modification  of  the 
prize  design  submitted  by  the  late  George  S.  Morri- 
son. The  original  competitive  designs  estimated  to 
cost  from  $370,000  to  $1,100,000  were  published  in 
Engineering  News  January  27,  1898.  It  was  built 
under  the  direction  of  Col.  John  Biddle,  Engineer 
Commissioner  of  the  District  of  Columbia.  "W.  J. 


SiS 

bb  at 

5  w 


90          CONCRETE  BRIDGES   AND   CULVERTS. 

Douglas.  Bridge  Engineer.     E.  P.  Casey  Consulting 
Architect. 

Big  Muddy  River  Bridge,  Illinois. 

Two  tracks  of  the  Illinois  Central  Railroad  are 
carried  over  Big  Muddy  River  near  Grand  Tower, 
Illinois,  on  a  new  three-span  concrete  arch  bridge. 
It  was  built  in  1903  to  replace  an  old  steel  bridge, 
and  for  this  reason  the  piers  remain  in  their  original 
location.  The  bridge  has  three  clear  openings  of 
140  feet,  and  a  total  length  of  463  feet  between  faces 
of  abutments.  It  is  32  feet  wide,  contains  12,000 
cubic  yards  of  concrete,  and  cost  complete  $125,000. 
The  arches  are  true  ellipses  with  semi-minor  axes  of 
30  feet.  The  old  piers  were  9  to  10  feet  in  thick- 
ness, and  the  new  ones,  which  were  built  around  the 
old  ones,  are  22  feet  thick.  The  main  arches  are 
solid  concrete,  the  only  reinforcing  being  in  the 
spandrel  arches  supporting  the  floor,  and  this  was 
used  for  convenience  in  erection.  As  built,  with 
spandrel  arches  and  openings,  the  cost  was  some- 
what greater  than  if  it  had  been  filled.  The  de- 
signer explains  that  open  spandrels  were  used  for 
the  purpose  of  reducing  the  load  on  the  foundations. 
Big  Muddy  River  Bridge  was  designed  by  II.  W. 
Parkhurst,  Engineer  for  the  Illinois  Central  Rail- 
road Company. 

Santa  Ana  Bridge,  California. 

This  structure  carries  the  new  line  of  the  San 
Pedro,  Los  Angeles  and  Salt  Lake  Railroad,  over 
Santa  Ana  River,  near  Riverside,  California.  The 


I 

i 


91 


fl 


S      „ 

w 


PLAIN  CONCRETE  ARCH  BRIDGES.  93 

bridge  has  a  total  length  of  984  feet,  and  the  deck 
is  55  feet  above  the  water.  It  was  built  during  the 
years  1902  to  1904  under  the  direction  of  Henry 
Hawgood,  who  was  then  Chief  Engineer  for  the 
above  railroad  company.  It  contains  eight  semi- 
circular arches  of  86  feet  clear  span,  and  two  end 
spans  of  38  feet.  The  piers  are  14  feet  in  thickness, 
making  the  distance  on  centers  of  main  piers  100 
feet.  It  is  made  of  solid  concrete  without  reinforce- 
ment, contains  12,500  cubic  yards  of  concrete  and 
cost  $185,300.  The  thickness  of  arch  at  crown  is  3 
feet  6  inches,  and  the  width  across  soffit  is  17  feet 
and  6  inches. 

A  letter  from  Mr.  Hawgood  to  the  author  in  ref- 
erence to  this  bridge  states  as  follows: — "The  Santa 
Ana  viaduct  has  given  entire  satisfaction  from  an 
operating  standpoint.  There  has  been  no  cost  for 
maintenance  during  the  five  years  it  has  been  in 
service,  whereas  a  steel  bridge  would  certainly  have 
involved  some  expense  during  the  same  period.  In 
positions  such  as  the  Santa  Ana  Viaduct  where 
there  is  no  limitation  as  to  headroom,  I  consider  the 
simple  concrete  structure  without  reinforcement  a 
better  structure  than  one  reinforced.  The  greater 
weight  of  concrete  required  forms  a  much  heavier 
mass  to  take  up  the  impact  of  heavy  high  speed 
trains.  The  absence  of  vibration  is  very  marked. 
It  is  a  parallel  condition  to  a  heavy  anvil  under  a 
steam  hammer — the  heavier  the  anvil,  the  longer  it 
will  last." 


94          CONCRETE   BRIDGES   AND   CULVERTS. 


TABLE  I 


LIST  OF  CONCRETE  BRIDGES 


1 

1 

2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
Hi 
17 
IS 
19 
20 
21 
22 
23 
21 
2f) 
2(5 
27 
2S 

LOCATION. 

Over. 

i 

02 

•8 

d 

& 

Length  of  Span,  ft. 

| 

Total  Length,  ft.  j 

Hudson  Mem.,  New  York. 

Spuvten  Duvvil. 
a              n 

1 

7 
1 

703 

108 
320 

177 

2840 

it          n          tt      tt 

Auckland,  N.  Z.  .                  

910 

? 

35 

n          <• 

4 

1 
5 

1 

^ 

2 
1 
1 

2 

1 
1 
1 
5 
2 
5 
2 
2 
1 
3 
1 
1 
3 
1 
2 

70 
280 
44 
233 
53 
230 
210 
211 
68 
187 
165 
164 
150 
82 
150 
120 
30 
144.6 
140 
141 
139 
60 
127.6 
20 

"so" 

22 
73 
26.5 
42 

87' 

"708 
'585 
"720 
',500 

Detroit  Avenue,  Cleveland  
Walnut  Lane,  Philadelphia  

Rocky  River..  .  . 
Wissahickon.  .  .  . 
Tsar 

Gruenwald  Bavaria 

T^lm,  Germany 

Railway  Yards  . 
Iller  River  . 

Kenipton,  Germany 

it        it 

Lautrach         " 

K        a 
Neckar           .    .  . 

32 
13.5 
16.4 
75 
41 
40 

18.5 
30 
14 
44 
30 
22.5 

280 

1341 

1450 
1450 
1450 

483 
150 
542 
542 

Neckarhausen,  Germany  
Munderkingen,  Wurtemburg  

Connecticut  Ave.,  Washington.  .  .  . 

«             it              tt 

Portland,  Pennsylvania  

Danube  

Rock  Creek  
it        it 

Delaware  River  . 
Thames  

«                  « 

a                  tt 

Vau  xhall,  London  

Grand  Tower,  Illinois  

Big  Muddy  River 
Danube  

Jnzighofen,  Germany  

Edrnondson  Ave.,  Baltimore  
Borrodale  Scotland 

Gwynns  River  .. 
tt          a 

Borrodale  Burn 
a            n 

a                a 

PLAIN  CONCRETE  ARCH  BRIDGES. 


95 


TABLE  I— Continued 


LIST  OF  CONCRETE  BRIDGES 


M 

3 

1 
•53 
H 

Form  of  Curve. 

| 

Highway  or  Railroad 

•4 

I 

Engineer. 

Reference. 
N.,  Eng.  News 
R.,     "      Record 

Number. 

80 

u 

40 
« 

tt 

60 
60 
60 
60 
20 
46 
54 

183 

•  t 

147 

H. 

H. 
it 

't 
IT. 

H. 

H. 

H. 
R.  R. 

£3,800,000 

Moiseeiff 

u 

N.,  Nov.    21,  '07 
R.,  Dec.     28,  '07 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 

1908 
it 

1909 
1906 

1904 
1905 
1906 

94 
94 
147 
147 

Sec;. 
C. 
E. 
C. 

'  C.'  ' 

208,300 

Felgate 
Webster 
Morsch 

262,000 

N.,  Jan.     31,  '07 
N.,  Jan.     31,  '07 
N.,  Feb.    23,  '05 
N.,  Mar.     15,  '06 

65,000 
45,000 

13.8 
15  8 
26 
52 
52 
31 
34 
34 

40 

Seg. 

1906 
1903 
1893 
1907 

R.  R. 
H. 
H. 
H. 

21,600 

Leibbrand 
Leibbrand 
Morrison 

N.,  May       2,  '07 

120 

'  C.'  ' 

c 

21,420 

850,000 

N.,  Mar.    26,  '08 

65 
65 
65 

El. 

1908 
1908 
1908 
1899 

R  R 

Bush 
Bush 
Bush 
Binnie 
Parkhurst 
Leibbrand 

R.,  Aug.    15,  '08 
R.,  Aug.    15,  '08 
R.,  Aug.    15,  '08 

R   R 

R  R 

33 

12.5 
60 
60 

45 

20 
70 
70 

E. 
Seg. 

C. 

1902 
1895 

1909 
« 

1898 

R.  R. 
H. 
H. 

125,000 
6,650 
183,300 

N.,  Nov.    12,  '03 
N.,  Sept.    17,  '96 
R.,  June  19,     '09 

R.  R. 

Simpson 

N.,  Feb.       9,  '99 

96          CONCRETE  BRIDGES  AND   CULVERTS. 


TABLE  I— Continued 


LIST  OF  CONCRETE  BRIDGES 


1 

% 

LOCATION. 

O.er. 

No.  of  Spans. 

Length  of  Span,  ft. 

| 

I 

9q 

Sixteenth  St  ,  Washington  

Piney  Creek.  .  .  . 

1 

125 

39 

272 

30 

Kirchheim,  Wurtemburg  
Hainsbur01  New  Jersey  

Neckar  
Paulins  Kill  .  .    . 

4 

5 

124.6 
120 

19 
60 

450 
1100 

39 

fl 

100 

1100 

?3 

Miltenburg,  Germany  

Main  

r 

112 

17.7 

733 

34 

c 

107 

35 
36 

Pittsburg  Pennsylvania 

Silver  Lake 

102 
100 

50 

600 

37 

n                             « 

Thebes  Illinois 

Mississippi 

e 

t. 

1 

80 
100 

40 
50 

?9 

«     '      a 

11 

65 

32.5 

40 

Danville  Illinois                          .  . 

Vermillion 

i 

100 

40 

330 

41 

2 

80 

30 

42 

43 

Mechanicsville,  New  York  

Anthony  Kill.  .  . 

9 

1 

100 

50 



14 

Imnau   Bavaria                           .  . 

Eyach 

1 

98 

9  8 

110 

45 

46 

Wyoming  Ave.,  Philadelphia  
Brookside  Park,  Cleveland  .  .    . 

Frankford  Creek 
Big  Creek  .  . 

2 
1 

98 
92 

28 
9 

200 
125 

47 

Riverside  California.          

Santa  Ana  

8 

86 

43 

984 

48 

«         « 

38 

19 

lf 

Boulevard  Philadelphia  

Tacony  Creek   .  . 

3 

80 

14 

350 

51 

Long  Kev  Florida.         

Atlantic  

180 

50 

25 

10500 

51 

Mannheim 

Neckar.  .        .    . 

1 

365 

rco 

Larimer  Ave     Pittsburg 

Beechwood  Boul 

1 

300 

53 

Spokane                          

Spokane  

1 

115 

791 

54 

1?,0 

60 

55 

tl 

« 

1 

100 

50 

190 

PLAIN  CONCRETE  ARCH  BRIDGES. 


97 


TABLE  I— Continued 


LIST  OF  CONCRETE  BRIDGES 


d 

25 
19 
34 
34 
23 

i 

i 

o 
•8 

1 

1 

1906 
S98 
1908 

Highway  or  Railroad 

M 

I 

Engineer. 

Reference. 
N.,  Eng.  News 
R.,     "      Record 

3 

|Z5 

50 
40 
115 
115 
22 

Par. 
Seg. 
C. 

H. 
H. 
R.  R. 

50,000 
46,600 

Douglas 

R.,  Jan.  26,  '07 
N.,  Mar.  29,  '00 
R.,  Aug.  15,  '08 

29 
30 
31 
32 
33 
34 
35 
36 
37 

Bush 

Seg. 

1899 

H. 

101,000 

Fleischman 

N.,  July  25,  '01 

54 
54 
28 
28 
33 
33 

70 
70 

C. 
C. 
C. 

c. 

1905 

R.  R. 

Brown 

R.,  May  6,  '05 

1903 

R.  R. 



Nobel 

N.,  Nov.  20,  '02 

38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
51 
52 
53 
54 
55 
56 

90 

1905 

R.  R. 

Duane 

R.,  Mar.  3,  '03 

El.  R 

N.,  Nov.  5,  '03 

8.2 
80 
12.7 
17.6 

'100 

15 

15 
32 
12 
55 

"30 
30 

Seg. 

"EI." 
c. 
c. 

Se, 

1896 
1908 
1905 
1904 
1904 
1908 
1904 

H. 
H. 
H. 
R.  R 
R.  R 
H. 
R.  R 

4,285 
102,000 

185,000 

Leibbrand 
Quimby 
Zesiger 
Hawgood 

N.,  Feb.  16,  '99 
R.,  Feb.  27,  '09 
N.,  May  10,  '06 
R.,  Sept.  9,  '05 

100,000 

Webster 
Carter 

'Whi'ted  " 
Ralston 

R.,  Mar.  13,  '09 
N.,  Oct.  19,  '05 
Proposed  
Projected  

1909 

« 
tl 

It 

H. 

« 

tt 

(t 

71 
it 

n 

140 

C. 



... 

1 

PART  II. 

Reinforced  Concrete  Arch  Bridges. 

Reinforced  concrete  arch  bridges  as  usually  built, 
are  a  combination  of  arch  and  beam,  and  contain 
most  of  the  properties  of  both  types,  the  arch  or 
beam  properties  predominating  according  as  they 
have  a  large  or  small  rise  in  proportion  to  their 
span.  Flat  arches  act  more  like  beams,  regardless 
of'  theory. 

Reinforced  concrete  was  first  considered  merely 
a  cheap  substitute  for  stone,  but  its  own  merits 
are  now  recognized  and  it  is  used  in  a  manner  ac- 
cording with  its  properties. 

A  principle  of  architectural  design  demands  that 
imitation  of  one  material  by  the  use  of  another 
shall  not  be  made,  and,  therefore,  in  designing  con- 
crete bridges,  there  should  be  no  effort  to  imitate 
stone,  but  to  treat  the  design  simply  and  truth- 
fully, keeping  all  lines  in  harmony  with  the  mate- 
rial used. 

The  extent  to  which  concrete  and  reinforced  con- 
crete are  now  being  used  in  preference  to  stone  or 
steel,  may  be  judged  from  the  fact  that,  during  the 
year  1908,  there  was  at  least  twenty  times  more 
cement  manufactured  and  sold  than  in  the  corre- 
sponding period,  ten  years  previous.  As  methods 
of  design  and  construction  become  generally  un- 
derstood and  as  workmen  become  more  accustomed 
to  handling  concrete,  there  will  be  a  still  greater 
number  of  bridges  built  of  this  material.  Long 


REINFORCED    CONCRETE    ARCH    BRIDGES.    101 

spans  exceeding  three  to  four  hundred  feet,  will 
probably  continue  to  be  framed  in  metal,  but  there 
is  reason  to  believe  that  all  ordinary  town  and 
county  bridges  and  the  majority  of  railroad  bridges 
will  be  built  as  permanent  structures. 

Reinforced  concrete  is  a  good  combination  of 
materials.  Concrete  has  a  high  compressive 
strength,  but  is  weak  in  tension.  Steel  rods  im- 
bedded in  concrete  have  a  high  tensile  strength, 
but  are  weak  in  compression.  The  steel,  therefore, 
strengthens  the  concrete,  and  the  concrete  stiffens 
the  steel,  the  strength  of  one  thus  supplementing 
the  weakness  of  the  other. 

Since  the  beginning  of  the  competitive  practice 
in  bridge  building,  many  bridges  have  been  built 
which  are  deficient  in  both  strength  and  design. 
There  is  no  doubt  that  competition  is  responsible 
for  many  economic  features  in  steel  bridge  design 
and  has  helped  to  a  great  extent  in  developing  eco- 
nomic methods.  It  was  found  about  the  year  1900, 
that  steel  bridges  were  being  built  entirely  too 
light  and  competition  was  responsible  for  the  con- 
dition. Previous  to  that  time,  the  various  bridge 
companies  were  accustomed  to  submit  competitive 
plans,  and  generally  the  lowest  bid  and  conse- 
quently the  weakest  bridge  was  the  one  accepted. 
From  that  date  the  policy  began  to  change,  and 
instead  of  calling  for  competitive  designs,  a  com- 
petent engineer  was  employed  to  prepare  plans  and 
competitive  prices  were  then  received  on  his  plans. 
The  policy  of  employing  an  engineer  whose  prin- 


102        CONCRETE   BRIDGES  AND   CULVERTS. 

cipal  motive  was  to  produce  an  economic  design, 
has  resulted  in  a  much  better  class  of  bridges  than 
under  the  old  competitive  system. 

Concrete  bridges  are  now  in  the  same  stage  of 
development  as  were  steel  bridges  ten  years  ago. 
Many  concrete  bridges  have  been  and  are  still  be- 
ing built,  which  are  lacking  in  architectural  de- 
sign and  some  are  lacking  in  strength.  The  prin- 
cipal reason  for  these  defects  is  that  reinforced 
concrete  bridges  are  obliged  to  compete  with  struc- 
tures of  wood  and  steel.  When  towns  and  other 
municipalities  realize  the  chances  they  are  taking 
in  accepting  competitive  designs,  the  method  of 
securing  an  acceptable  one  will  then  be  changed 
and  a  competent  engineer  will  be  employed  to  pre- 
pare the  plans.  Competitive  prices  will  then  be  re- 
ceived on  these  plans,  but  competition  will  cause  no 
reduction  of  the  cost  by  weakening  any  parts  of 
the  bridge.  At  the  present  time,  stone  and  con- 
crete bridges  exist,  having  factors  of  safety  varying 
from  three  to  one  hundred  and  fifty,  and  there  is, 
therefore,  a  very  evident  need  for  better  and  more 
rational  methods  of  design. 

Historical  Outline. 

Since  the  early  days  of  stone  bridge  building, 
rods  and  bands  of  hoop  iron  have  been  used  near 
the  extrados  of  the  arch  from  the  piers  and  abut- 
ments, to  or  slightly  beyond  the  point  of  rupture. 
It  was  found  when  the  temporary  arch  centers  were 
removed,  that  the  arch  settled  at  the  crown  and 


REINFORCED    CONCRETE   ARCH   BRIDGES.    103 

there  was  a  tendency  for  the  masonry  joints  to 
open  at  the  extrados  haunches.  To  prevent  these 
joints  from  opening,  iron  rods  have  long  been  used. 
There  was  then  no  general  effort  made  to  strengthen 
the  masonry  arch,  excepting  as  stated  above.  Con- 
crete arches  are  reinforced  with  metal  not  only  at 
the  extrados  from  the  piers  to  the  points  of  rup- 
ture, but  are  also  strengthened  at  all  places  where 
there  is  any  possibility  of  tension  in  the  arch  ring. 
Jean  Monier  first  began  using  reinforced  concrete 
in  Germany  in  the  year  1867,  by  making  large 
flower  pots  and  urns  of  cement  and  concrete  with  a 
single  layer  of  wire  netting  embedded  therein. 
Monier  was  a  gardener,  but  he  foresaw  a  success- 
ful future  for  this  combination,  and  in  the  next 
ten  years  he  built  a  number  of  tanks,  bins  and 
other  small  structures  of  the  composite  material, 
and  secured  patents  from  the  German  Government 
on  his  invention.  Introduction  of  this  construction 
in  Germany  was  slow,  and  it  was  not  until  1894 
that  the  Monier  patents  were  introduced  in  the 
United  States.  This  system  of  reinforced  concrete 
contained  a  single  layer  of  wire  mesh  with  wires 
of  the  same  size  in  both  directions.  Professor 
Melan  realized  the  weakness  of  the  Monier  system 
and  patented  another  and  improved  method  of  re- 
inforcing arches,  by  which  curved  steel  ribs  were 
placed  lengthwise  of  the  arch  and  imbedded  in  the 
concrete  two  or  three  feet  apart.  In  his  first  de- 
signs, curved  1  beams  were  used  and  are  still  used 
under  his  patents  for  small  spans.  For  larger  spans 


104        CONCRETE   BRIDGES   AND   CULVERTS. 

with  a  greater  thickness  of  arch  ring,  he  proposed 
a  system  of  light  latticed  girders  spaced  from  three 
to  five  feet  apart,  which  system  is  still  in  use. 
These  patents  were  introduced  in  the  United  States 
by  Herr.von  Emperger  in  the  year  1893,  and  under 
these  patents  many  of  America's  best  concrete 
bridges  are  built.  In  the  year  1894,  when  American 
engineers  began  to  seriously  consider  building  and 
replacing  old  bridges  in  the  newT  type,  it  was  esti- 
mated that  Europe  had  not  less  than  two  hundred 
of  these  bridges  built  mostly  on  the  Monier  system. 
("A  bridge  which  is  believed  to  be  the  first  of  rein- 
;forced  concrete  in  the  United  States,  was  built  in 
\  Golden  Gate  Park,  San  Francisco,  in  1889.  It  has 
/  a  20-foot  span,  4  feet  3  inches  rise,  and  a  width  of 
v64  feet.  It  is  an  ornamental  bridge  with  curved 
wing  walls  built  with  imitation  rough  stone  finish. 
A  second  one  in  the  same  park  and  of  similar  de- 
sign was  built  in  1891.  In  1895  a  70-foot  span  arch 
was  built  by  Ilerr  von  Emperger,  carrying  a  drive- 
way over  Park  Avenue  in  Eden  Park,  Cincinnati. 
The  bridge  is  located  in  the  park  at  a  place  much 
frequented,  and  an  effort  was  made  to  make  it  both 
strong  and  beautiful.  The  balustrade  is  highly  or- 
namental and  the  spandrel  walls  are  decorated  with 
panels.  The  intrados  of  the  arch  is  much  flatter 
than  appears  necessary  and  certainly  a  greater  rise 
would  have  presented  a  more  pleasing  effect. 

During  .the  first  ten  years  after  the  introduction 
of  the  Melan  patents  in  the  United  States,  there 
were  not  more  than  a  hundred  reinforced  concrete 


REINFORCED    CONCRETE   ARCH   BRIDGES.    105 

bridges  built.  The  fact  that  a  more  general  intro- 
duction of  this  system  was  not  made,  was  probably 
due  to  the  lack  of  more  definite  knowledge  and 
data  in  reference  to  the  action  and  behavior  of  this 
construction  under  live  loads.  European  engineers 
were  likewise  embarrassed  by  lack  of  knowledge, 
so  much  so,  that  during  the  years  1890  to  1895,  the 
Austrian  Government  undertook  extensive  experi- 
ments on  full-sized  concrete  arches.  The  result  of 
these  experiments  was  entirely  satisfactory,  and 
complete  reports  of  the  investigations  were  pub- 
lished in  many  of  the  engineering  journals  of  Amer- 
ica and  Europe.  From  the  completion  of  these  ex- 
periments in  1895  to  the  present  time,  the  building 
of  bridges  in  concrete  and  reinforced  concrete  has 
been  on  the  increase,  and  there  are  now  more  than 
a  thousand  of  these  bridges  in  the  United  States. 
Previous  to  these  experiments,  no  satisfactory 
progress  was  made  either  here  or  abroad. 

At  first  it  was  customary  to  use  reinforcing  steel 
in  the  arch  ring  only,  but  later  structures  and  most 
of  those  now  being  built  have  metal  reinforcement 
throughout.  Masonry  bridges  and  buildings  are  still 
existing  that  have  stood  for  many  centuries,  while 
steel  bridges  built  less  than  forty  years  ago,  have 
already  worn  or  rusted  out  and  have  been  replaced. 
Two  of  these  bridges  have  already  been  illustrated 
in  Part  I  of  this  book,  and  there  are  positive  rec- 
ords of  many  others  quite  as  ancient  which  are  still 
in  existence.  Pont  du  Gard,  an  old  Roman  aque- 
duct bringing  water  to  the  city  of  Nimes,  France, 


106        CONCRETE  BRIDGES  AND   CULVERTS. 

is  supposed  to  have  been  built  about  the  time  of 
Augustus  in  the  year  19  B.  C.  The  Aqueduct  of 
Vejus,  consisting  of  a  series  of  high  arches,  and 
the  dome  of  the  Pantheon  at  Rome,  with  a  span  of 
140  feet,  are  at  least  1,800  years  old  and  all  of 
these  structures  are  even  now  in  a  fairly  good  con- 
dition. These  and  many  others  quite  as  old  are 
built  of  coarse  concrete  masonry. 

Several  American  railroad  companies,  after  re- 
peatedly renewing  their  metal  bridges  to  support 
increased  loads  and  rolling  stock,  have  at  last  re- 
sorted to  building  their  bridges  in  masonry,  know- 
ing that  when  properly  built,  they  will  remain  as 
permanent  structures  for  centuries. 

Advantages  of  Reinforced  Concrete. 

The  general  advantages  of  masonry  as  compared 
to  steel  framing  have  already  been  referred  to  on 
page  1.  These  advantages  referred  particularly 
to  plain  concrete  rather  than  to  reinforced  con- 
crete bridges.  It  was  stated  there,  that  arch  bridges 
of  solid  concrete  were  superior  to  all  others,  and 
particularly  superior  to  arches  where  tension  oc- 
curs in  any  part  of  the  arch  ring.  In  pointing  out 
the  commendable  qualities  of  solid  concrete,  it  is 
not  intended  to  deny  the  merits  of  reinforced  con- 
crete. On  the  other  hand,  reinforced  concrete 
arches  have  some  decided  advantages  over  solid 
concrete.  Some  of  these  advantages  are  as  follows : 
(1)  Working  units  for  reinforced  concrete  may  be 
higher  than  for  plain  concrete. 


REINFORCED    COXCRETE    ARCH   BRIDGES.    107 

(2)  Higher  units  produce  a  thinner  arch  ring,  and 

consequently  less  dead  load  and  lighter  abut- 
ments. 

(3)  Flat  arches  may  be  safely  used,  which  would 

be  impossible  in  solid  concrete. 

(4)  Because  of  their  lighter  weight,  it  is  practica- 

ble to  build  spans  of  much  greater  length. 

(5)  All  cracks  of  every  description  can  be  avoided 

in  reinforced  concrete  arches. 

(6)  They  have  the  strength  of  steel  with  the  solid- 

ity and  substantial  appearance  of  stone. 
Bridges    of   both    plain    and   reinforced    concrete 
have  also  the  following  merits : — 

(1)  They  have  no  noise   or  vibration  and  are  not 

only  cheaper  but  more  durable  than  stone. 

(2)  Concrete    bridges   with  solid   decks   permit  the 

use  of  ordinary  ties  for  railroad  tracks,  which 
cannot  be  used  on  steel  bridges  with  open 
decks. 

(3)  The  floors  of  concrete  street  bridges  over  rail- 

road tracks  are  not  damaged  by  the  action 
of  gas  and  fumes  from  locomotives,  as  is  the 
framing  of  these  bridges  when  built  in  steel. 

(4)  Concrete  bridges  require  but  very  little  skilled 

labor. 

(5)  A  concrete  arch   bridge  so  designed  that  ten- 

sion cannot  occur  at  any  time  or  under  any 
condition  of  loading,  is  the  most  permanent 
bridge  of  all.  If  no  tension  occurs,  cracks 
will  not  form  to  permit  moisture  to  reach 
and  corrode  the  reinforcing  steel,  and  when 


108        CONCRETE  BRIDGES  AND   CULVERTS. 

the  metal  is  permanently  protected  and 
secure  from  the  atmosphere  and  moisture,  it 
should  endure  for  centuries. 

Deck  bridges  are  in  nearly  all  cases  preferable  to 
those  where  the  travel  is  carried  between  lines  of 
side  trussing  and  beneath  systems  of  overhead  brac- 
ing. Such  truss  and  bracing  systems  are  a  danger 
and  menace  to  travel,  particularly  on  crowded  thor- 
oughfares, and  obstruct  the  space  required  for 
vehicles.  Trussing  and  bracing  are  also  an  ob- 
struction to  observation  and  the  clearance  required 
through  the  bridge  prevents  the  use  of  lateral  brac- 
ing necessary  to  stiffen  the  frame.  Concrete  arch 
bridges,  when  deck  structures,  are  free  from  the 
disadvantages  mentioned  above.  Through  bridges 
should  never  under  any  condition  be  used  for  im- 
portant locations  unless  the  underneath  clearance 
or  structural  requirements  positively  prohibit  the 
use  of  a  deck  bridge. 

For  all  ordinary  locations  and  length  of  span, 
there  appears,  therefore,  to  be  no  good  or  sufficient 
reason  for  building  unsightly  frame  structures 
when  more  permanent  and  artistic  ones  can  be  made 
at  the  same  cost. 

Adhesion  and  Bond. 

Rich  cement  concrete  in  wrhich  iron  or  steel  is 
embedded  has  an  adhesion  thereto  of  from  500  to 
600  pounds  per  square  inch  of  exposed  surface.  Ad- 
hesion of  concrete  to  metal  occurs  only  when  the 
metal  is  thoroughly  embedded  and  the  concrete  has 


REINFORCED    CONCRETE   ARCH   BRIDGES.    109 

opportunity  to  surround  and  grip  the  bars.  If  a 
metal  bar  is  placed  simply  in  contact  with  soft 
concrete  there  will  be  but  little  adhesion.  For  the 
purpose  of  illustration,  if  steel  plates  are  placed 
on  edge  and  concrete  filled  in  between,  but  not  un- 
der or  above  them,  after  the  concrete  has  hardened 
it  will  be  a  comparatively  easy  matter  to  loosen 
the  concrete  and  break  the  adhesion.  This  weak- 
ness is  due  to  the  fact  that  the  concrete  is  simply 
in  contact  with  the  metal  but  does  not  grip  or  sur- 
round it.  In  contrast  to  this  condition,  if  a  bar 
be  thoroughly  embedded  and  surrounded  wTith  rich 
concrete,  it  will  adhere  so  securely  to  the  rod,  that 
a  pull  of  from  500  to  600  pounds  for  every  square 
inch  in  contact  will  be  required  to  extricate  the 
rod  from  its  bed.  In  order  to  develop  the  full 
strength  of  the  rod  up  to  its  elastic  limit,  it  is 
necessary  that  the  embedded  length  must  at  least 
equal  twenty  to  twenty-five  times  the  diameter  of 
the  rod.  This  is  on  the  assumption  of  perfect  ad- 
hesion between  the  metal  and  concrete.  The  mix- 
ture as  ordinarily  used,  instead  of  fine  mortar,  con- 
tains more  or  less  voids,  which  may  be  considered 
equal  to  50%  of  the  entire  surface  in  contact.  To 
allow  for  watersoaking,  a  still  further  reduction 
of  50%  must  be  made.  In  ordinary  work  as  found 
in  actual  structures,  the  adhesion  between  the  con- 
crete and  metal,  instead  of  being  from  500  to  600 
pounds  per  square  inch,  as  for  fine  test  samples, 
would,  therefore,  not  exceed  from  125  to  150 
pounds  per  square  inch.  By  using  a  factor  of 


110        CONCRETE   BRIDGES  AND   CULVERTS. 

safety  of  five  a  working  adhesive  unit  will  not  ex- 
ceed from  30  to  40  pounds  per  square  inch  of  sur- 
face in  contact.  The  length,  therefore,  that  rods 
must  be  embedded  in  ordinary  concrete  to  develop 
their  full  strength  up  to  the  elastic  limit  is  about 
four  times  twenty-five,  or  one  hundred  times  the 
diameter  of  the  rod. 

It  has  been  positively  proven  by  numerous  ex- 
periments that  concrete  adheres  as  securely  to 
smooth  rods  as  it  does  to  rough  ones.  Frequent 
and  continued  shocks  and  vibrations  tend  to  de- 
stroy the  union  between  the  two  materials,  and  ex- 
periments show  that  continuous  watersoaking  from 
six  to  twelve  months  reduces  the  adhesion  by  about 
100%.  Poor  workmanship  in  placing  and  ramming 
the  concrete  is  also  probable  and  for  these  reasons, 
it  is  desirable  to  use  reinforcing  rods  that  are 
roughened  or  twisted,  so  the  bar  may  have  a  direct 
mechanical  grip  on  the  concrete  in  addition  to  its 
adhesion.  "When  this  roughening  of  the  bars  is 
secured  without  decreasing  their  cross-sectional 
area,  the  entire  area  of  the  bar  is  then  available 
for  tension  and  no  strength  is  lost  by  the  expedi- 
ent. Roughening  the  bars  can,  therefore,  do  no 
harm  and  it  may  be  a  source  of  extra  strength.  As- 
suming that  the  rough  rods  cost  more  than  plain 
ones,  the  consideration  in  making  a  choice  between 
the  two,  is  simply  whether  the  extra  expense  for 
rough  rods  is  warranted  by  the  additional  strength 
that  they  may  give.  AVhilf3  watersoaking  decreases 
the  adhesion  between  the  two  materials,  the  upper 


REINFORCED   CONCRETE   ARCH   BRIDGES.    Ill 

concrete  surfaces  are  usually  waterproofed,  and 
the  probability  is,  that  instead  of  weakening  from 
watersoaking,  the  strength  of  the  concrete  and  its 
adhesion  to  the  steel  will  increase.  The  conclusion, 
however,  is  that  rough  rods  are  preferable.  They 
cost  but  little  more,  can  do  no  harm  and  may  be  a 
benefit. 

Metal  Reinforcement. 

Reinforcing   steel    in    concrete    bridges    is    intro- 
duced for  any  or  all  of  the  following  reasons : — 

(1)  To   resist  tensile   stresses  due  to  bending  mo- 

ments, 

(2)  To  prevent   cracks   occurring   from   change   of 

temperature, 

(3)  To  form  a  temporary  working  platform  at  the 

roadway  level. 

There  is  no  sufficient  reason  from  a  scientific 
standpoint  for  the  use  of  high  tension  bars  or 
rods  for  concrete  reinforcement.  After  years  of 
investigation  and  experiment,  brittle  metal  wras  dis- 
carded for  structural  use  and  the  only  reason  for 
a  return  to  the  use  of  high  tension  bars  now,  is  a 
commercial  one  and  not  scientific.  It  is  well  known 
that  in  re-rolling  bars  to  produce  surface  roughen- 
ing, the  tensile  strength  of  the  metal  is  increased 
Instead  of  admitting  the  inferior  quality  of  their 
products,  interested  parties  have  endeavored  to  ex- 
plain that  this  increase  in  tensile  strength,  and  cor- 
responding decrease  in  ductility  is  a  benefit. 

Medium    steel    with    an    elastic  limit   of  32,000 
pounds  per  square  inch,  or  soft  steel  with  a  corre- 


112        CONCRETE   BRIDGES  AND   CULVERTS. 

spending  elastic  limit  of  28,000  pounds,  are  the 
proper  grades  of  metal  for  all  ordinary  concrete 
reinforcement.  These  may  safely  be  stressed  up 
to  half  their  elastic  limit  under  working  loads.  If, 
for  any  sufficient  reason  a  high  tension  metal  is 
desirable,  then  some  grade  of  wire  is  preferable  to 
bars.  It  is  difficult,  however,  to  secure  good  con- 
tact between  wire  mesh  and  concrete,  for  the  small 
openings  in  the  mesh  make  it  difficult  to  tamp  the 
two  materials  well  together.  If  a  mesh  must  be 
used,  then  a  large  mesh  is  preferable  to  a  smaller 
one.  In  nearly  all  positions,  whether  tensile  stresses 
are  liable  to  occur  or  not,  the  presence  of  metal 
in  concrete  will  add  to  its  strength  and  perma- 
nence. Only  in  such  places  where  there  is  insuffi- 
cient space  for  its  insertion,  will  it  be  a  detriment. 
The  rule  generally  is  "when  in  doubt,  use  rein- 
forcement ' '. 

The  old  Monier  system  of  arch  reinforcement, 
consisting  of  a  single  layer  of  wire  mesh  with  wires 
of  the  same  size  in  each  direction,  is  evidently 
wrong  in  principle.  The  amount  of  metal  required 
crosswise  and  longitudinally  of  the  arch  is  not  nec- 
essarily the  same,  for  the  area  in  each  case  must 
be  suited  to  its  need.  For  resisting  bending  mo- 
ments in  the  arch  ring,  when  the  line  of  pressure 
falls  outside  of  the  middle  third,  the  size  of  rods 
will  depend  on  the  magnitude  of  the  bending  mo- 
ments. 

It  was  customary  at  first  to  reinforce  only  the 
arch  ring,  but  now  all  parts  of  reinforced  concrete 


REINFORCED    CONCRETE   ARCH    BRIDGES.    113 

bridges,  excepting  perhaps  the  balustrade  and  other 
ornamental  features,  are  provided  with  metal  for 
the  purpose  of  better  uniting  the  whole  into  a  solid 
monolith.  It  is  particularly  desirable  that  rein- 
forcement be  placed  at  all  points  where  local  loads 
are  liable  under  any  circumstances  to  produce 
bending  or  tension.  Where  cross  spandrel  walls 
bear  upon  the  arch  ring,  these  walls  should  not 
only  be  well  anchored  to  the  arch,  but  additional 
metal  may  be  required  beneath  these  concentrated 
loads.  The  best  practice  at  the  present  time  in 
reinforcing  concrete  arch  rings  is  to  use  two  com- 
plete systems,  one  at  the  extrados  and  the  other 
at  the  intrados  of  the  arch.  Some  designers  prefer 
to  reinforce  the  extrados  only  from  the  springs  to, 
or  a  little  beyond  the  point  of  rupture,  omitting 
the  metal  at  the  extrados  crown.  The  saving  by 
this  omission  is  not  great  and  generally  is  not  suffi- 
cient to  warrant  it. 

At  all  points  where  light  walls  or  sections  join 
to  heavier  concrete  masses,  heavy  reinforcement 
should  be  used.  In  setting  and  drying,  concrete 
acts  much  in  the  same  way  as  cast  iron,  and  unless 
the  light  sections  are  well  tied  to  the  heavier  ones, 
cracks  at  the  junction  will  occur.  This  is  illus- 
trated where  ring  walls  join  to  the  abutments.  If 
for  any  reason,  it  is  impracticable  to  anchor  the 
wing  walls  to  the  abutment  face,  it  is  then  prefer- 
able to  leave  an  open  joint,  for  otherwise  an  irreg- 
ular crack  will  occur,  showing  weakness  either  in 
the  design  or  in  the  construction. 


114        CONCRETE   BRIDGES  AND   CULVERTS. 

As  the  amount  of  adhesion  between  steel  and  con- 
crete depends  directly  upon  the  amount  of  steel 
surface  in  contact  with  the  concrete,  it  is  prefer- 
able for  securing  the  greatest  bond,  to  use  a  larger 
number  of  small  bars  rather  than  a  smaller  number 
of  larger  ones.  It  is  desirable  also  to  have  the 
cracks  in  the  concrete  as  small  as  possible,  so  water 
will  not  enter  the  cracks  and  corrode  the  metal. 
Upon  this  feature  the  duration  of  a  concrete  struc- 
ture depends.  Tf  water  is  allowed  to  soak  into  the 
cracks  and  corrode  the  reinforcing  metal,  it  will 
then  be  only  a  few  years  until  the  strength  of  the 
member  will  be  destroyed  by  rust.  It  is  necessary, 
therefore,  that  sufficient  reinforcing  metal  be  used 
in  order  that  cracks  will  not  be  excessive.  Several 
leading  designers  of  reinforced  concrete  are  now 
specifying  that  tension  in  the  concrete  shall  be 
considered,  and  enough  metal  used  so  the  tension 
in  the  concrete  will  not  exceed  a  safe  unit,  which 
is  usually  placed  at  about  50  pounds  per  square 
inch  on  the  cross-sectional  area  of  the  concrete  in 
tension.  The  object  in  this  is  to  prevent  cracks 
from  forming  and  to  exclude  all  moisture  from  the 
metal.  This  is  doubtless  the  ideal  condition,  for 
when  perfectly  embedded  and  protected  from  mois- 
ture, steel  is  known  to  be  indefinitely  preserved. 
When  insufficient  steel  is  used,  large  cracks  will 
form  on  the  tension  side  and  the  bridge  is  then 
no  more  a  permanent  one  than  an  ordinary  steel 
bridge,  or  not  even  as  permanent.  When  a  steel 
bridge  is  exposed  to  moisture  the  steel  can  be  ex- 


REINFORCED    CONCRETE   ARCH   BRIDGES.    115 

amined  and  painted,  whereas  in  a  reinforced  con- 
crete bridge,  the  steel  is  concealed  from  view,  can- 
not be  inspected,  and  its  collapse  is  the  first  warn- 
ing given  that  the  metal  reinforcement  has  been 
destroyed.  The  best  results  are,  therefore,  secured 
by  allowing  no  cracks  whatever,  but  if  cracks  must 
form,  to  have  these  cracks  so  small  that  water  can- 
not enter  them.  Tt  is  better  to  have  a  large  num- 
ber of  very  small  cracks  than  a  small  number  of 
large  ones. 

A  requirement  upon  which  the  strength  of  rein- 
forced concrete  directly  depends,  is  the  amount  of 
contact  between  the  two  composing  materials. 
Every  effort  should  be  made  to  have  this  contact 
as  perfect  and  complete  as  possible.  In  deciding 
upon  a  working  unit  for  adhesion  of  concrete  to 
steel,  it  is  customary  to  consider  that  imperfect 
workmanship  in  ordinary  structures  wrill  cause  only 
about  one-half  of  the  exposed  metal  surface  to  be 
actually  gripped  by  the  cement.  If  a  higher  de- 
gree of  workmanship  be  secured,  then  the  strength 
of  the  structure  will  be  increased  accordingly.  It 
is  considered  that  watersoaking  still  further  de- 
creases the  adhesion  by  another  100%.  Therefore, 
if  perfect  adhesion  on  rich  samples  between  the  two 
materials  is  from  500  to  600  pounds  per  square 
inch,  the  ultimate  adhesion  in  actual  structures  can- 
not be  taken  greater  than  from  125  to  150  pounds 
per  square  inch.  To  develop  the  full  tensile  strength 
of  bars  embedded  in  concrete,  it  is  easy,  therefore, 
*  compute  the  length  that  these  bars  must  be  em- 


116        CONCRETE   BRIDGES  AND   CULVERTS. 

bedded.  Using  an  ultimate  adhesive  unit  for  ordi- 
nary structures  of  150  pounds  per  square  inch,  one 
inch  square  bars  would  be  gripped  to  the  extent 
of  600  pounds  per  lineal  inch  of  bar.  Therefore,  to 
secure  the  full  elastic  strength  of  the  bar  up  to 
-32,000,  the  rod  must  be  embedded  a  number  of 
inches,  equal  to  32,000  divided  by  6,000,  or  53 
inches.  Where  arch  rings  join  to  piers  and  abut- 
ments, it  is  customary  to  run  the  reinforcing  steel 
well  into  the  piers  to  develop  the  full  strength  of 
the  metal. 

Experiments  show  that  adhesion  to  steel  is  much 
greater  before  the  steel  is  painted  than  afterward. 
A  slight  coating  of  rust  has  been  found  to  add  to, 
rather  than  to  detract  from,  the  adhesive  strength. 
Loose  scales  or  Hakes  of  rust  must  not  be  permit- 
ted, but  a  slight  rusting  is  no  disadvantage.  Ex- 
periments have  been  made  on  rusted  steel  imbedded 
in  rich  cement,  and  after  a  period  of  several  months 
when  the  steel  was  removed  and  the  cement  broken 
away,  it  was  found  that  the  steel  appeared  clean 
and  free  from  even  the  slight  rusting  that  existed 
when  it  was  first  imbedded. 

Light  reinforcing  frames  are  frequently  used  in 
the  spandrels  of  reinforced  concrete  bridges,  not 
only  to  strengthen  the  concrete,  but  also  to  provide 
a  temporary  working  platform  at  the  roadway 
level.  This  plan  is  illustrated  by  the  Illinois  Cen- 
tral Railroad  Company's  bridge  over  Big  Muddy 
River  near  Grand  Tower,  Illinois.  Bridges  built 
by  Herr  Wunsch  in  Germany  were  mostly  of  this 


REINFORCED    CONCRETE   ARCH   BRIDGES.    117 

type.  The  metal  in  such  cases  must  have  sufficient 
strength  to  act  as  compressive  members.  In  the 
Big  Muddy  River  bridge,  the  engineer  used  old 
rails  for  the  spandrel  frames,  and  when  completed, 
these  were  encased  by  the  concrete  spandrel  col- 
umns. 

Reinforcing  Systems. 

The  principal  reason  for  the  existence  of  the 
many  patented  systems  for  concrete  reinforcement 
is  the  patent  royalty  secured  therefrom.  There  are 
a  few  essential  requirements,  and  where  these  are 
fulfilled,  the  reinforcement  is  satisfactory.  Chief 
among  these  requirements  are : — 

(1)  The  metal  shall  be  rough  or  have  a  mechanical 

union  with  the  concrete, 

(2)  Reinforced  beams  shall  have  stirrups  for  trans- 

mitting shear  components  from  the  main  ten- 
sion members  into  the  web  of  the  beam. 
In  connection  with  the  latter  requirement,  it  is 
preferable  that  the  stirrups  be  rigidly  connected 
to  the  tension  member,  in  order  to  secure  a  positive 
transmittal  of  the  shear  components. 

The  various  reinforcing  systems  may  be  roughly 
classified  under  two  headings. 
(1.)   Slab  Reinforcement, 
(2)  Beam  Reinforcement. 

Under  the  first  heading  are  included  the  various 
kinds  of  expanded  metal.  Light  rods  are  suitable 
for  slabs,  as  are  also  twisted  bars  and  plain  flats 
with  rivet  heads  thereon.  For  beam  reinforce- 
ment, the  opportunity  for  patented  systems  is 


118        CONCRETE  BRIDGES  AND   CULVERTS. 

greater,  and  a  large  number  are  now  on  the  mar- 
ket. Among  these  may  be  mentioned  Twisted  rods. 
Corrugated  bars,  Diamond  bars,  Thacher  bars,  Cup 
bars,  Twisted  Lug  bars,  etc.  All  of  these  are  rods 
and  bars  without  provision  for  stirrup  connection. 
In  addition  to  these,  there  is  quite  a  variety  of 
patented  bars  on  the  market,  either  in  the  form 
of  truss  frames  or  with  stirrup  connections.  In  this 
latter  class  may  be  placed  the  Kahn  bar,  the  Cum- 
mings  Girder  Frame,  the  Unit  Reinforcing  Frame, 
the  Luten  Truss,  the  Monolith  Frame,  the  General 
Fireprooling  Company's  Girder  Frame  and  others. 
For  slab  reinforcement,  a  coarse  wire  with  its 
high  tensile  strength  and  corresponding  high 
elastic  limit,  is  economical.  It  does  not  have  the 
disadvantage  of  high  tension  bars,  for  while  bars 
are  brittle  and  lack  ductility,  wire  is  elastic  and 
has  always  been  and  probably  will  continue  to  be 
a  desirable  tensile  metal.  It  bends  easily,  will  not 
crack  in  handling  and  gives  a  large  external  con- 
tact area  in  proportion  to  its  section.  Certain  kinds 
of  wire  mesh  have  the  principal  strands  in  one 
direction,  united  by  a  lighter  weave  at  right  angles 
to  them.  This  type  of  wire  mesh  is  made  with  the 
principal  wires  in  various  sizes  and  is  well  suited 
for  reinforcing  bridge  floors.  Where  floor  panels 
are  square  and  floor  beams  in  both  directions,  it 
is  then  economical  to  use  a  wire  mesh  with  wires 
of  the  same  size  in  each  direction.  Most  of  the 
various  expanded  metal  systems,  while  they  have 
a  lower  tensile  strength,  have  sufficient  stiffness  to 


REINFORCED    CONCRETE   ARCH   BRIDGES.    119 

support  their  own  weight  during  construction,  and 
are  rougher  and  have  a  greater  mechanical  bond 
than  wire.  An  excellent  example,  showing  the  vari- 
ous methods  of  reinforcement  for  concrete  bridges 
is  a  ribbed  design,  for  Grand  Avenue  Viaduct  in 
Milwaukee,  shown  in  Figure  27  and  more  fully  de- 
scribed in  the  Engineering  News,  February  14, 
1907. 

As  the  shearing  stress  in  curved  arch  slabs  is 
quite  small,  there  is  but  little  need  for  metal  in 
the  web.  The  Melan  system  has  continuous  lines 
of  double  angle  bars  at  the  extrados  and  the  in- 
trados  of  the  arch,  connected  by  light  lattice  work, 
and  these  are  manufactured  complete  in  the  struc- 
tural shop  and  shipped  to  the  bridge  site  ready  for 
erection.  These  frames  are  blocked  up  vertically 
on  the  arch  centers  from  three  to  five  feet  apart 
crosswise  of  the  bridge,  and  they  are  connected  at 
intervals  with  bars  or  frames  which  take  the  place 
of  expansion  rods.  These  shop-riveted  frames  con- 
siderably simplify  the  work  of  field  erection  and 
avoid  the  complexity  and  confusion  which  is  liable 
to  occur  when  a  large  number  of  disconnected  small 
bars  are  used,  but  much  of  the  web  material  and 
the  shop  labor  of  riveting  is  unnecessary  for  re- 
sisting stresses.  In  some  of  the  designs,  Mr.  Thacher 
has  used  plain  flat  bars  adjacent  to  the  extrados 
and  intrados  placed  about  two  feet  apart.  These 
bars  are  roughened  by  having  rivets  driven  at  fre- 
quent intervals,  rivet  heads  projecting  to  form  the 
mechanical  bond. 


120        CONCRETE   BRIDGES  AND   CULVERTS. 

The  Kahn  bar  with  light  connected  diagonals,  is 
well  suited  for  arch  reinforcement,  as  the  web 
members  securely  tie  the  reinforcing  bar  into  the 
body  of  the  arch,  but  any  system  of  rough  bars  or 
rods  which  are  completely  imbedded  in  and  sur- 
rounded with  concrete  and  which  have  the  neces- 
sary cross-sectional  area,  regardless  of  whether  they 
have  a  web  connection  or  not,  are  suitable  for  con- 
crete arch  reinforcement. 

Concrete  Composition. 

It  is  customary  with  some  engineers  to  specify 
several  degrees  of  richness  for  the  concrete  in  a 
single  bridge.  Mixtures  varying  from  one  part  of 
cement  with  two  of  sand  and  three  of  gravel  and 
stone,  varying  through  several  different  grades  to 
corresponding  mixtures  of  1,  5  and  10,  are  all 
specified  in  the  same  bridge,  the  richer  concrete  for 
the  spandrel  or  arch  ring  and  the  poorer  for  the 
abutment  foundation.  The  policy  is  generally  un- 
warranted. Anyone  who  has  observed  the  ordinary 
methods  used,  and  the  way  in  which  concrete  goes 
into  structures,  should  realize  that  exact  methods 
which  can  reasonably  be  applied  to  single  truss 
systems,  and  specifications  for  various  grades  of 
metal,  are  not  appropriate  or  suitable  for  use  in 
the  design  of  concrete  bridges.  Generally  it  is  quite 
sufficient  to  specify  only  one  or  two  kinds  of  con- 
crete mixtures,  the  richer  for  the  superstructure 
and  the  poorer  grade,  if  another,  for  the  founda- 
tion. Examination  of  test  records  on  the  strength 


REINFORCED    CONCRETE   ARCH   BRIDGES.     121 

of  concrete  mixtures,  varying  from  1,  2  and  3  to 
1,  3  and  6,  does  not  show  enough  variance  in 
strength  to  warrant  a  change  of  working  unit. 
Therefore,  instead  of  several  mixtures  with  only 
slight  variations,  it  is  better  to  specify  a  single 
mixture.  It  is  frequently  cheaper  for  the  con- 
tractor to  put  in  all  mixtures  of  the  richer  grade, 
than  to  make  numerous  changes.  A  more  impor- 
tant consideration  than  the  quality  of  the  concrete, 
is  the  securing  of  contact  between  the  concrete  and 
the  metal.  In  proportion  as  this  is  well  or  poorly 
done,  the  permanency  of  the  bridge  depends. 

Loads. 

The  principal  loads  on  masonry  arches  are  the 
dead  weight  of  the  arch  itself  and  the  superimposed 
material  above  it.  It  is  better  to  consider  only 
vertical  loads  as  acting  on  ordinary  earth  filled  flat 
arches,  for  the  conjugate  horizontal  forces  are  small 
and  may  be  neglected.  The  amount  of  horizontal 
thrust  from  earth  filling  is  indefinite,  for  the  earth 
will  recede  more  or  less  horizontally,  allowing  the 
arch  to  settle  at  the  crown.  Therefore,  neglecting 
these  horizontal  earth  pressures  is  an  assumption 
on  the  side  of  safety.  It  must  be  noted,  however, 
that  the  above  statements  apply  only  to  flat  arches 
when  the  proportion  of  rise  to  span  is  small.  When 
the  arch  has  a  greater  rise  equal  to  or  approaching 
half  the  span,  the  conditions  are  greatly  changed, 
for  below  the  point  of  rupture  the  horizontal  thrusts 
are  so  great  that  solid  masonry  filling  is  required. 


122        CONCRETE   BRIDGES  AND   CULVERTS. 

The  side  retaining  walls  of  earth  filled  arches  fre- 
quently act  as  arch  ribs  and  carry  a  large  propor- 
tion of  the  weight  of  the  earth  filling.  The  distri- 
bution of  loads  in  earth  filled  arches  is  uncertain 
and  the  proportion  borne  separately  by  the  arch 
ring  and  the  side  walls  acting  as  arch  ribs,  is  un- 
certain. To  avoid  this  uncertainty  some  engineers 
are  now  designing  the  side  retaining  walls  with 
one  or  more  expansion  joints  in  each  wall,  to  pre- 
vent these  side  Avails  from  having  any  arch  action. 
The  entire  dead  weight  and  imposed  loads  must 
then  be  supported  by  the  arch  ring.  There  is  no 
doubt  that  the  side  retaining  walls  are  capable  of 
supporting  large  loads  as  arch  ribs,  but  it  is  im- 
portant to  know  definitely  which  members  of  a 
structure  are  in  action.  Any  type  of  construction 
in  which  the  action  of  stresses  is  indefinite,  is  in 
many  ways  undesirable.  The  condition  is  similar 
to  that  of  multiple  systems  for  metal  truss  bridges. 
Multiple  systems  are  no  doubt  economical,  but  it 
is  usually  impossible  to  know  what  proportion  of 
the  load  is  carried  by  each  system.  This  lack  of 
definite  knowledge  is  often  the  cause  of  failure,  and 
it  is  desirable  in  the  design  of  masonry  as  well  as 
steel  structures  to  have  the  condition  of  loads  as 
nearly  fixed  as  possible.  For  this  reason  many 
arches  are  designed  with  cross-spandrel  walls  elim- 
inating entirely  any  possibility  of  external  hori- 
zontal pressure  on  the  arch  ring. 

The  weight   of  earth   filling  varies   according  to 
its  nature  from  100  to  120  pounds  per  cubic  foot, 


REINFORCED    CONCRETE  ARCH  BRIDGES.    123 

and  the  weight  of  concrete  from  130  to  160  pounds 
per  cubic  foot,  depending  upon  the  density  of  the 
stone.  Other  loads  such  as  that  of  pavement,  rail- 
ing, water  pipes,  etc.,  must  be  taken  according  to 
their  actual  weights.  Approximate  general  rules 
for  moving  live  loads  are  as  follows : — 

(a)  Light  carriage  travel  is  equivalent  to  100  pounds 

per  square  foot. 

(b)  Heavy    carriage    travel    is    equivalent    to    200 

pounds  per  square  foot. 

(c)  Electric    railroad   travel   is    equivalent    to    500 

pounds  per  square  foot. 

(d)  Steam   railroad    travel   is    equivalent   to    1,000 

pounds  per  square  foot. 

There  is  usually  sufficient  earth  filling  above  the 
arch  ring  to  distribute  any  concentrated  loads,  and 
particularly  for  railroad  bridges  where  the  ties  and 
rails  assist  in  spreading  the  load  out  over  a  greater 
area.  It  is  usually  safe,  therefore,  to  consider  all 
live  loads  as  uniformly  distributed.  These  rules 
apply  only  to  earth  filled  arches,  for  the  loads  on 
arch  rings  which  have  open  cross-spandrel  cham- 
bers or  arcades  occur  beneath  the  spandrel  walls, 
and  are  plainly  concentrated  loads.  The  system 
of  loads  should  be  carefully  considered  for  each 
case,  and  the  designer  should  be  satisfied  in  refer- 
ence to  the  safety  of  his  assumptions,  for  local  loads 
might  easily  occur  which  would  require  special  pro- 
vision. 

The  bending  moments  on  arch  rings  for  moving 
loads  are  a  maximum  when  the  uniform  live  load 


124        CONCRETE  BRIDGES  AND   CULVERTS. 

covers  from  two-fifths  to  three-fifths  of  the  span, 
but  it  is  usually  considered  as  covering  one-half  of 
the  span. 

The  weight  of  loaded  electric  cars  varies  from 
1,000  to  3,000  pounds  per  lineal  foot  of  track,  one- 
half  of  this  load  being  borne  on  each  rail.  The 
weight  of  ordinary  light  electric  cars  fully  loaded 
will  not  exceed  1,000  pounds  per  lineal  foot,  but  it 
is  now  customary  to  proportion  the  better  class  of 
street  railroad  bridges  to  carry  loaded  freight  cars 
which  it  is  often  convenient  to  switch  over  electric 
railroad  tracks.  The  additional  cost  of  proportion- 
ing bridges  for  this  extra  load  is  comparatively 
small.  The  electric  railroad  companies  themselves 
so  often  require  large  quantities  of  coal  delivered 
at  their  power  plants,  that  they  are  usually  will- 
ing to  pay  the  extra  cost  of  a  bridge  over  which 
their  tracks  run,  in  order  to  have  coal  cars  deliv- 
ered directly  to  their  plants. 

Temperature  stresses  in  masonry  arch  rings  are 
frequently  as  large  or  even  larger  than  the  bending 
stresses  from  partial  live  loads.  Masonry  bridges 
are  not  subject  to  so  great  a  range  of  temperature 
as  metal  bridges,  for  masonry  is  a  poorer  conductor 
of  heat  than  metal  and  the  intrados  of  an  arch  is 
not  exposed  to  the  direct  rays  of  the  sun,  neither 
is  the  extrados  or  any  .part  of  the  arch  ring  ex- 
cepting the  ends  appearing  at  the  spandrel.  For 
this  reason  it  is  safe  to  assume  a  maximum  tem- 
perature range  of  from  50  to  60  degrees  between 
the  highest  and  the  lowest  temperatures  of  the 


REINFORCED    CONCRETE   ARCH   BRIDGES.   125 

arch  material.  Temperature  stresses  may  be  en- 
tirely eliminated  by  the  use  of  hinges  at  the  springs 
and  crown,  but  the  practice  with  American  engin- 
eers is  to  spend  more  money  in  making  the  founda- 
tions secure,  and  thereby  avoid  the  need  of  hinges. 
The  money  that  would  be  spent  on  building  hinges 
is  put  into  the  foundations. 

As  temperature  rises,  the  arch  expands  and  rises 
at  the  crown,  but  when  the  temperature  falls,  the 
arch  contracts  and  it  must  necessarily  fall  at  the 
crown.  This  rise  and  fall  of  the  arch,  due  to  at- 
mospheric conditions,  is  the  cause  of  temperature 
stresses. 

Addition  must  be  made  to  the  live  loads  to  pro- 
vide for  the  effect  of  impact.  The  amount  of  this 
impact  is  determined  from  the  formula 

Impact  load= 

L+D 

where  L  is  the  live  load  and  D  the  total  dead  load 
per  horizontal  square  foot  on  the  arch. 

Units — Ultimate  and  Working. 

Permissible  working  units  for  plain  concrete 
arches  have  already  been  given  in  Part  I.  Rein- 
forced concrete  arches  may  have  higher  values, 
owing  partly  to  the  fact  that  the  reinforcing  steel 
will  resist  some  compression  and  also  because  rein- 
forced masonry  is  a  more  secure  monolith.  Con- 
crete has  an  ultimate  compressive  stress  of  from 
2,000  to  2,800  pounds  per  square  inch.  A  working 
unit  for  plain  concrete  in  compression  was  given 


126        CONCRETE  BRIDGES  AND   CULVERTS. 

at  400  pounds  per  square  inch;  for  reinforced  con- 
crete it  is  safe  to  assume  500  pounds  per  square 
inch  for  combined,  direct  and  live  load  bending 
stresses.  For  combined,  direct,  bending  and  tem- 
perature stresses,  it  is  safe  to  assume  a  working 
unit  of  from  600  to  700  pounds  per  square  inch. 

American  engineers  generally  are  accustomed  to 
using  much  lower  working  units  in  concrete  than 
are  used  by  European  engineers.  There  is  probably 
sufficient  reason  for  these  lower  units,  for  the  qual- 
ity of  work  done  in  America  is  not  so  fine  as  is 
produced  in  France  and  Germany.  In  designing 
the  Grand  Avenue  bridge,  now  being  built  in  Mil- 
waukee, the  concrete  working  units  used  were  500 
pounds  per  square  inch,  and  600  pounds  including 
temperature  stresses.  Perfect  adhesion  of  rich 
concrete  to  steel  varies  from  500  to  600  pounds  per 
square  inch.  It  has  already  been  shown  under  the 
heading  "Adhesion",  that  30  pounds  per  square 
inch  of  exposed  surface  is  a  safe  and  usual  work- 
ing adhesive  unit. 

The  ultimate  shearing  strength  of  concrete  is  400 
pounds  per  square  inch  and  a  safe  working  unit  is 
50  pounds  per  square  inch. 

A  safe  working  stress  for  steel  in  compression  is 
one-half  its  elastic  strength,  or  14,000  pounds  per 
square  inch  for  soft  steel  and  16,000  pounds  per 
square  inch  for  medium  steel.  The  ultimate  tensile 
strength  of  good  concrete  is  200  pounds  per  square 
inch,  and  for  the  purpose  of  preventing  cracks 
forming  on  the  tension  side  of  beams  or  members 


REINFORCED    CONCRETE   ARCH   BRIDGES.    127 

subject  to  bending,  provision  may  be  made  for 
tension  in  the  concrete,  not  exceeding  50  pounds 
per  square  inch.  The  object  in  this  is  plainly  to 
prevent  cracks  from  forming,  which  would  admit 
water  or  moisture  and  expose  the  metal  to  the  dan- 
ger of  corrosion.  The  provision  is  a  safe  one,  but 
as  the  modulus  of  elasticity  for  steel  is  not  more 
than  twenty  times  greater  than  for  concrete,  the 
steel  in  the  tension  side  of  the  beam  would  then 
be  stressed  to  only  twenty  times  the  tension  allowed 
on  the  concrete,  or  20  times  50,  which  is  1,000 
pounds  per  square  inch,  instead  of  16,000  pounds 
per  square  inch. 

Some  engineers  propose  a  method  of  proportion- 
ing concrete  sections  by  the  use  of  ultimate  units 
applied  to  three  or  four  times  the  actual  loads.  This 
method  is  inconsistent.  Bridge  engineers  have  long 
been  accustomed  to  using  safe  working  units  for 
structures  which  are  only  a  fraction  of  the  ultimate 
values,  using  different  working  values  where  neces- 
sary for  the  dead  and  the  live  loads.  The  same  system 
used  in  designing  steel  bridges  should  be  applied  also 
to  concrete  bridges,  and  all  sections  proportioned 
according  to  safe  working  units  after  addition  has 
been  made  to  the  live  loads  for  impact.  It  is  evi- 
dent that  when  a  tension  unit  of  16,000  pounds  per 
square  inch  is  used  for  dead  load  stresses  and  a 
corresponding  tension  unit  of  only  8,000  pounds 
for  live  load  stresses,  that  provision  is  made  by 
these  varying  units  for  impact  amounting  to  100%. 
It  is  simpler  and  more  accurate  to  follow  the  method 


128        CONCRETE  BRIDGES  AND   CULVERTS. 

of  the  more  recent  steel  bridge  specifications  and 
apply  impact  addition,  using  the  same  unit  stresses 
for  both  dead  and  live  loads. 

Theory  of  Arches. 

The  exact  theory  of  arches  is  very  complex.  Sev- 
eral comprehensive  books  have  been  written  on 
the  subject  and  the  theory  will  be  referred  to  only 
briefly  here.  For  a  full  discussion  and  explanation 
of  the  various  theories,  the  reader  is  referred  to 
any  of  the  mathematical  treatises  on  the  elastic 
arch.  The  subject  has  been  treated  generally  by 
two  methods,  the  analytical  and  the  graphical. 
Most,  if  not  all  writers  and  designers  using  the 
analytical  method  follow  the  theory  as  developed 
and  explained  by  Professor  Charles  E.  Green  in  his 
book  entitled  "Trusses  and  Arches",  while  expo- 
nents of  the  graphical  method  use  the  one  out- 
lined by  Professor  William  Cain  in  his  ''Theory  of 
Elastic  Arches". 

The  complexity  of  the  subject  is  responsible  to 
a  great  extent  for  the  lack  of  a  more  general  in- 
troduction of  reinforced  concrete  arches.  They  are 
really  a  combination  of  arch  and  beam.  Plain  con- 
crete arches  have  already  been  discussed  in  Part  I, 
and  reinforced  concrete  beams  are  considered  in 
Part  III.  The  reinforced  concrete  arch  is  propor- 
tioned to  act  both  in  direct  compression  and  as  a 
beam,  to  resist  bending  stresses  from  uneven  load- 
ing on  the  arch  ring. 

The  arch  is  distinguished  from  the  beam  by  hav- 
ing horizontal  or  inclined  thrusts  at  the  springs,  in 


REINFORCED    CONCRETE    ARCH   BRIDGES.    129 

addition  to  the  Arertical  reaction  of  the  abutments. 
Arches  are  classified  under  three  headings  accord- 
ing as  they  are  fixed  or  hinged- 

(1)  Arches  with  no  hinges, 

(2)  Arches  with  twro  hinges  at  the  springs, 

(3)  Arches    with    hinges    at    the    two    springs    and 

hinge  at  the  crown. 

They  are  classified  also  under  two  general  heads 
into  (1)  Slab  Arches  and  (2)  Ribbed  Arches. 

The  stress  conditions  in  the  arch  vary  greatly, 
depending  upon  the  presence  or  absence  of  hinges. 
The  space  allotted  to  this  book  wrill  not  permit  of 
more  than  a  very  brief  review  of  the  principles 
involved.  The  principal  part  of  the  computation 
for  a  reinforced  concrete  arch  consists  in  finding 

(a)  the  horizontal  thrust, 

(b)  the  end  reactions  and 

(c)  the  bending  moments  at  various  points  in  the 

span. 

After  these  haAre  been  found,  it  is  then  a  compara- 
tively easy  matter  to  proportion  the  metal  and  con- 
crete to  resist  the  stresses.  The  method  consists  in 
drawing  the  correct  line  of  pressure  for  the  given 
arch  arid  loading,  and  determining  its  proper  posi- 
tion in  the  arch  ring.  When  this  has  been  done,  it 
is  easy  to  find  the  bending  moment  at  any  point  of 
the  arch. 

Most  of  the  uncertainties  of  masonry  arches 
which  have  been  enumerated  in  Part  I  apply  equally 
to  reinforced  arches.  The  elastic  theory  applies 
not  only  to  arches  in  which  bending  moments  are 


130        CONCRETE   BRIDGES  AND   CULVERTS. 

resisted  by  the  arch  ring,  but  may  be  used  also 
for  arches  of  solid  concrete  with  no  tension  in  any 
part  of  the  arch  ring  or  where  the  line  of  pressure 
lies  in  all  cases  within  the  middle  third  of  its  depth. 
The  theory  is  applicable  both  for  two-hinged  and 
for  fixed  end  arches. 

rches  with  fixed  ends  have  five  unknown  quan- 
tities, 

(a)  equal  horizontal  thrusts  at  either  end, 

(b)  two  vertical  end  reactions  and 

(c)  two  bending  moments  at  the  springs. 

Where  there  are  no  hinges  in  the  arch,  the  reac- 
tions are  not  transferred  to  the  abutments  in  ac- 
cordance with  the  law  of  the  lever.  Since  there 
are  five  unknown  quantities,  there  must  in  addition 
to  the  two  equations  of  equilibrium,  2x=0  and  ^—0 
be  three  more  equations  found.  These  are  deter- 
mined from  the  conditions  of  equilibrium  for  fixed 
end  arches,  which  are  as  follows : — 

(1)  The  angle  of  inclination  that  the  springs  make 

with  each  other  must  not  change. 

(2)  The   relative    elevation    of   the    two    end   abut- 

ments must  not  change,  and 

(3)  The  length  of  span  must  not  change. 

These  are  mathematically  expressed  by  the  formu- 
lae : — 

2$  n  M= 0,  2$  n  MX     0,  2%  n  Mi/  =0. 
In  the  above  formulae,  M  is  the  general  value  of 
the  bending  moments,  n  the  length  of  a  short  por- 
tion of  the  arch  ring,  and   x  and  y,  the  horizontal 
and  vertical  coordinates  to  the  center  of  n,  meas- 


REINFORCED    CONCRETE   ARCH   BRIDGES.    131 

ured  from  the  origin  at  the  springs  A  or  B.  Fixed 
end  arches  have  high  temperature  stresses,  two  to 
four  times  greater  than  for  two-hinged  arches. 

The  abutment  reactions  for  arches  with  either 
two  or  three  hinges,  follow  the  law  of  the  lever, 
which  greatly  simplifies  the  mathematical  calcula- 
tions. 

Two-hinged  arches  have  only  three  sets  of  un- 
known forces, 

(1)  The  horizontal  reaction  and 

(2)  The  two  vertical  end  reactions. 

As  there  are  hinges  at  the  end  and  a  condition  of 
continuity  cannot  exist  there,  the  two  additional 
unknown  quantities,  the  two  unknown  bending  mo- 
ments at  the  springs  do  not  now  exist.  This  is  the 
theoretical  assumption,  but  it  is  not  exact,  for  even 
with  pin  bearings  at  the  end,  there  is  a  large 
amount  of  friction  on  the  pins  and  the  bending  mo- 
ments will  not  entirely  disappear.  The  assumption, 
however,  for  two-hinged  arches  is  that  there  are 
only  three  sets  of  unknown  forces.  Therefore,  in 
addition  to  the  two  usual  equations  of  equilibrium 
2x=Q  and  2y  =  0,  there  is  only  one  other  equa- 
tion required,  and  this  can  be  found  from  the  con- 
dition that  the  length  of  span  must  not  change.  The 
span  length  should  not  change  or  no  sliding  of 
either  abutment  should  occur  in  order  that  the  arch 
ring  between  the  springs  shall  remain  intact. 
The  third  equation  required  for  the  solution  of 


132        CONCRETE   BRIDGES  AND   CULVERTS. 

the  two-hinged  arch  is,  therefore,  expressed  as  fol- 
lows : — 


Hinged  arches  are  not  frequently  built  in  America, 
but  some  designers  for  the  purpose  of  simplifying 
calculations,  consider  the  arch  ring  as  hinged  at 
the  springs. 

The  condition  of  stress  in  three-hinged  arches  is 
definite,  for  the  moments  both  at  the  springs  and 
crown  are  zero,  and  the  position  of  the  line  of  pres- 
sure is,  therefore,  fixed  at  these  three  points.  Tho 
equations  of  equilibrium  for  three-hinged  arches 
are,  therefore  :  — 


The  thrusts,  bending  moments  and  shears  may  bo 
found  most  easily  by  Professor  Cain's  graphical 
method,  after  which  the  section  may  be  most  easily 
proportioned  analytically.  It  has  already  been 
stated  that  the  graphical  method  consists  in  draw- 
ing the  correct  line  of  pressure  for  the  given  arch 
and  loading  and  determining  its  proper  position  in 
the  arch  ring. 

The  following  method  is  used  for  determining 
the  form  of  arch  and  the  thickness  of  the  arch  ring 
for  uniform  loading.  It  avoids  the  usual  trial 
method  given  in  Part  I  for  solid  concrete  arches. 
The  position  of  the  springs  must  first  be  assumed 
as  well  as  an  approximate  crown  thickness  and  the 
depth  of  earth  filling  above  it.  The  remaining 
height  from  spring  to  crown  intrados  will  be  the 


REINFORCED   CONCRETE   ARCH   BRIDGES.    133 

rise   of  the   arch.      The   method   depends   upon   the 

equation,  M—  HT,  where 

M  is  the  bending  moment, 

H  the   crown  thrust   or  pole  distance   of  the  force 

polygon,  and 
T  the  vertical  ordinate  to  the  pressure  curve  at  the 

point  where  the  moment  is  taken. 
The  bending  moment  at  the  center  is  the  same  as 
for  a  simple  beam  and  dividing  this  moment  by  the 
arch  rise  gives  the  crown  thrust  or  pole  distance 
H.  The  bending  moment  at  any  other  point  of  the 
arch  is  equal  to  the  pole  distance  IT  multiplied  by 
the  vertical  intercept  at  that  point  in  the  funicular 
polygon.  The  moments  are,  therefore,  computed 
for  as  many  points  as  desired  and  dividing  these 
moments  by  the  pole  distance  H,  which  has  already 
been  found,  gives  the  required  ordinates  T  to  the 
funicular  polygon,  which  is  the  line  of  pressure  for 
the  full  assumed  loading.  The  pressure  curve  is 
then  plotted  from  the  ordinates  found  and  this  will 
give  a  curve  for  uniform  loads. 

The  height  T  referred  to  above  is  the  distance 
to  the  line  of  pressure  measured  from  a  horizontal 
line  through  the  point  of  rupture,  which  is  not  nec- 
essarily at  the  abutment  face.  The  correct  crown 
thrust  cannot  be  obtained  by  using  a  distance  T  to 
any  point  below  the  point  of  rupture.  When  the 
point  of  rupture  falls  within  the  abutment  face, 
the  span  length  must  be  taken  as  the  distance  be- 
tween the  points  of  rupture,  and  not  the  clear  dis- 
tance between  abutments. 


134        CONCRETE   BRIDGES  AND   CULVERTS. 

For  full  dead  and  live  loads,  the  line  of  pressure 
should  wherever  possible,  lie  within  the  middle 
third  of  the  arch  ring,  and  reinforcement  used  only 
for  resisting  bending  stresses  due  to  partial  live 
loads.  In  Figure  26,  the  weight  of  the  arch  ring 
may  be  assumed  at  its  mean  thickness  at  the  quar- 
ter point,  and  the  arch  ring  weight  assumed  ap- 
proximately as  a  uniform  load.  The  weight  of  earth 
filling,  pavement  and  other  material  between  the 


Fig.  26 

extrados  and  roadway  level,  as  well  as  the  uniform 
live  load,  is  also  uniform,  and  the  center  bending 
moment  for  these  uniform  loads  is  expressed  by  the 
equation: 

M    w  s2 

M=  - 

8 
For  a  parabolic    arch,   the    spandrel    area    shown 


REINFORCED    CONCRETE   ARCH   BRIDGES.    135 

O  "R 

hatched  in  Figure  26  is  equal  to  -  — .  The  center  of 

6 

gravity  of  this  area  is  equal  to  one-eighth  of  the 
span  length  from  the  abutment  face.  Therefore, 
the  bending  moment  at  the  center  from  spandrel 

25  R  S2 
filling  is  equal  to   .     The  total  moment  is, 

JLU 

therefore,  equal  to  the  sum  of  moments  from  uni- 
form loads  and  from  the  spandrel  filling.  Dividing 
the  center  moment  by  the  rise  gives  the  crown 
thrust  or  pole  distance  II  for  the  force  polygon. 
This  is  a  very  convenient  analytical  method  for 
determining  the  correct  arch  form  for  any  system 
or  arrangement  of  loads.  A  combination  of  the  an- 
alytical with  the  graphical  method  will  simplify 
computation,  as  some  results,  like  finding  the  crown 
thrust,  may  be  determined  most  easily  by  the  an- 
alytical process. 

In  practice,  it  is  usually  sufficient  to  find  the 
sum  of  all  moments  and  thrusts  at  three  different 
points — the  center,  the  quarter  points  and  springs. 

The  thickness  of  arch  ring  at  other  points  below 
the  crown  must  be  such  that  the  vertical  heights  D, 
shall  not  be  less  than  at  the  crown. 

The  bending  moment  at  any  point  of  the  arch 
ring  from  partial  loading  is  equal  to  the  pole  dis- 
tance or  horizontal  thrust  at  the  center,  multiplied 
by  the  vertical  intercept* between  the  neutral  plane 
and  the  line  of  pressure  at  the  point  considered. 
The  correct  position  of  the  line  of  pressure  for 
partial  loading  will  already  have  been  drawn  upon 


136        CONCRETE  BRIDGES  AND   CULVERTS. 

the  arch  ring,  and  the  vertical  intercept  may  be 
scaled  and  will  be  positive  or  negative  according 
as  the  pressure  curve  lies  above  or  below  the  neu- 
tral axis  of  the  arch. 

The  determination  of  the  thrusts  and  moments 
may  be  simplified  by  considering  the  arch  as  a  par- 
abola. This  is  approximately  true  when  the  rise 
is  small  in  comparison  to  the  span. 

The  stability  of  an  arch  is  secured  when  it  will 
resist  the  stresses  resulting  from  thrust  and  bend- 
ing from  any  system  of  loads,  when  the  line  of 
pressure  is  drawn  in  such  a  position  as  to  produce 
the  least  possible  bending  moment,  or  when  the 
line  of  pressure  is  drawn  the  nearest  possible  to  the 
center  line  of  the  arch. 

General   Design. 

The  introduction  of  bridges  of  combined  metal 
and  concrete  has  thrown  open  a  wide  field  for  im- 
provement in  design.  So  long  as  it  was  necessary 
to  build  bridges  of  stone,  the  art  showed  no  great 
improvement  over  the  work  of  the  ancients.  In 
recent  years,  however,  the  increased  production  of 
cement  with  its  decreased  cost,  as  well  as  the  in- 
vention of  improved  stone-crushing  machinery  and 
appliances  for  mixing  concrete,  have  tended  to 
make  larger  structures  possible,  even  in  solid  ma- 
sonry. The  greatest  progress  in  the  art  has  been 
made  since  the  completion  of  the  Austrian  experi- 
ments iii  1895.  Reinforced  concrete  has  made  it 
possible  to  discard  old,  conventional  forms  and  to 
introduce  new  and  lighter  types  of  bridges  sup- 


REINFORCED    CONCRETE   ARCH   BRIDGES.    137 

ported  by  arch  ribs,  carrying  open  spandrel  framing 
to  support  the  roadway.  The  enormous  reduction 
in  the  dead  weight  of  the  superstructure  has  caused 
a  proportionately  large  saving  in  the  foundations. 
A  large  number  of  improved  methods  of  design 
have  already  been  tried  successfully  and  there  is 
prospect  of  additional  progress  in  the  future.  "With 
the  new  material  designers  are  following  to  some 
extent  the  outlines  used  for  metal  bridges,  so  there 
are  now  numerous  examples  of  bridges  built  in  con- 
crete-steel, not  only  in  the  form  of  light  ribbed 
arches,  but  also  as  solid  and  ribbed  cantilevers, 
girders,  trusses,  etc.  The  new  material  is,  in  fact, 
being  used  according  as  its  own  properties  will  per- 
mit. 

The    general    subject    of    arch    bridge    design    is 
divided  into  four  parts, 

(1)  The  parapet  or  deck, 

(2)  The  spandrels, 

(3)  The  arch  ring  and 

(4)  Temporary  arch  centers. 

In  beginning  the  general  design,  the  final  object 
should  at  all  times  be  kept  in  view.  The  first  and 
chief  object  in  building  all  bridges  is  to  construct 
and  support  a  platform  at  the  proper  elevation,  of 
sufficient  capacity  to  safely  and  securely  conduct 
travel  over  certain  openings.  A  second  object 
which  is  too  often  neglected,  is  the  desirability  of 
making  the  bridge  pleasing  in  appearance,  in  har- 
mony with  its  surroundings  and  a  credit  to  its 
builders. 


138        CONCRETE  BRIDGES  AND   CULVERTS. 

When  once  started,  the  design  should  be  contin- 
ued in  logical  sequence.  The  width  of  bridge  and 
the  kind  of  pavement  required,  should  be  selected 
with  the  necessary  filling  beneath  the  pavement  to 
support  the  roadway  or  the  railroad  ties.  After 
deciding  upon  the  kind  of  deck  required,  the  most 
economical  method  of  supporting  this  deck  must 
be  determined.  It  may  be  carried  on  solid  earth 
filling  or  on  a  series  of  walls  or  columns,  and  these 
may  be  continued  to  the  ground  in  the  form  of 
a  trestle,  provided  the  height  from  deck  to  ground 
is  small.  If  the  height  be  great,  these  walls  or 
columns  may  then  be  supported  on  other  ribs  or 
frames,  such  as  arches  or  trusses,  and  the  loads 
from  these  may  in  turn  be  transmitted  to  the 
ground  through  walls  or  piers  of  the  most  econom- 
ical form.  There  is  no  good  reason  why  the  span- 
drel columns  of  a  concrete  bridge  cannot  be  sup- 
ported in  other  ways,  excepting  on  slab  or  ribbed 
arches.  Trussed  frames  or  girders  are  possible 
forms,  though  they  would  not  be  as  pleasing  in 
appearance  as  a  continuous  arch.  It  is  possible 
that  arches  with  double  ribs  or  drums  separated 
by  systems  of  framing  may  be  used,  following  the 
outline  of  a  double-braced  metal  arch.  If  the  de- 
sign is  developed  in  successive  steps,  beginning 
with  the  roadway  platform,  and  transmitting  the 
loads  continuously  in  the  most  economical  man- 
ner through  various  kinds  of  framing  into  the 
foundations,  the  result  will  be  both  scientific  in  con- 
struction and  satisfying  to  the  engineer.  It  is  a 


REINFORCED    CONCRETE   ARCH   BRIDGES.    139 

deplorable  fact  that  the  design  of  many  bridges 
is  begun  by  first  locating  the  foundations  and  de- 
veloping the  design  upward  from  the  ground,  in- 
stead of  from  the  deck  downward.  This  one  error 
accounts  for  the  absence  of  economy  in  many  struc- 
tures. 

The  old  empirical  rules  for  masonry  arches, 
which  required  more  masonry  in  the  abutments 
than  in  the  arch,  are  unscientific  and  useless  for 
reinforced  concrete.  All  through  bridges  are  ob- 
jectionable. They  are  a  menace  and  an  obstruction 
to  travel,  are  lacking  in  lateral  stiffness,  and  the 
trusses  or  framing  interfere  with  the  river  view, 
which  is  generally  and  should  always  be  an  inter- 
esting feature  of  a  river  bridge. 

If  a  bridge  has  several  spans  and  one  span  has 
movable  bascule  leaves  or  other  kind  of  draw,  the 
outline  of  the  draw  span  should  conform  and  har- 
monize with  the  rest  of  the  bridge  and  its  pres- 
ence should  be  indicated  by '  piers  or  towers  at 
either  side  of  the  opening.  The  underneath  out- 
line for  double  bascule  leaves  in  a  single  span  may 
easily  be  made  in  the  form  of  a  continuous  arch, 
corresponding  to  the  intrados  curves  of  other  spans 
in  the  bridge. 

Unsymmetrical  arch  spans  may  be  used  at  the 
ends  of  viaducts  crossing  deep  ravines.  They  cause 
a  large  saving  in  the  abutments  by  permitting 
higher  springs  at  the  abutments  than  at  the  piers. 
The  half  shore  span  adjoining  the  pier  may  be  made 
with  intrados  curve  to  correspond  with  the  next 


140        CONCRETE   BRIDGES  AND   CULVERTS. 

adjoining  span,  thus  producing  symmetry  about  the 
pier  center.  As  the  end  arch  span  lacks  symmetry 
in  the  arch,  it  is  necessary  for  appearance,  that  the 
design  shall  be  symmetrical  about  the  pier. 

The  Kissinger  Bridge,  twelve  miles  southeast 
from  AVabash,  Indiana,  is  of  unusual  design.  It 
has  a  IG-foot  concrete  roadway  slab  balanced  on 
a  single  center  concrete  web  12  inches  in  thickness, 
supported  on  a  segmental  concrete  arch,  8  feet  in 
width.  It  is  a  single  span  highway  bridge,  with 
60-foot  opening  and  was  built  in  1907. 

All  towrn  or  city  bridges  should  have  open  cham- 
bers beneath  the  floor  for  pipes  and  wires.  They 
may  either  have  removable  iron  covers,  or  be  paved 
over,  with  manholes  or  entrances  provided  at  either 
end. 

Hinged  Arches. 

There  is  a  difference  of  opinion  with  regard  to 
the  use  of  hinged  or  fixed  arches  for  masonry 
bridges.  Hinges,  by  which  is  meant  the  insertion 
of  heavy  stone  or  metal  blocks  at  or  near  the  cen- 
ter line  of  the  arch,  remove  one  of  the  principal 
uncertainties  of  arch  construction,  by  fixing  the 
position  of  the  line  of  pressure  at  the  springs.  The 
presence  of  a  hinge  at  the  crown  tends  to  consid- 
erably reduce  the  rigidity  and  increase  deflection, 
and  is  not  alwajTs  to  be  recommended.  Hinges  may 
be  introduced  at  the  springs  in  such  a  manner  as 
to  insure  absolutely  within  small  limits  the  posi- 
tion of  the  line  of  pressure  there.  Fixed  ends  tend 
to  greatly  increase  the  amount  of  temperature 


REINFORCED    CONCRETE   ARCH   BRIDGES.    141 

stresses  and  they  have  no  advantages  over  hinged 
ends.  Alter  the  centers  are  removed  and  the  arch 
ring  has  come  to  or  nearly  to  its  final  position,  the 
open  joints  at  the  hinges  should  then  be  filled  solid 
with  cement,  so  the  entire  cross-section  at  the 
hinges  will  be  available  for  full  loading.  The  pres- 
ence of  hinges  or  the  assumption  of  their  presence 
at  the  springs,  simplifies  the  computations  and  re- 
moves one  of  the  chief  uncertainties  of  concrete 
arch  design.  The  American  practice  has  been  to 
avoid  any  extra  expenditure  on  hinges,  but  to  put 
it  into  the  foundations,  insuring  their  stability 
against  movement.  There  are  numerous  unfortu- 
nate cases  where  the  foundations  have  been  in- 
sufficient. Several  spans  of  a  bridge  over  the  Illi- 
nois River  at  Peoria  were  recently  destroyed,  owing 
to  the  undermining  of  foundations.  Hinges  are  de- 
sirable chiefly  where  it  is  known  that  the  soil  is 
yielding  and  the  abutments  are  liable  to  recede  lat- 
erally, allowing  the  arch  to  fall  at  the  crown,  and 
cause  unsightly  and  possibly  dangerous  cracks.  A 
method  employed  by  certain  German  engineers  is 
to  place  hinges  at  the  point  of  rupture.  This  was 
done  in  a  bridge  built  at  Kempten,  Bavaria,  over 
the  Iller  River,  and  described  in  the  Engineering 
News,  May  2,  1907. 

Ribbed  Arches. 

The  principal  economy  in  reinforced  concrete 
bridges  comes  from  the  use  of  ribbed  arches.  Most 
of  the  surplus  material,  both  in  the  structure  itself, 
and  in  the  spandrel  filling,  may  then  be  eliminated, 


142        CONCRETE  BRIDGES  AND   CULVERTS. 

and  as  weight  of  superstructure  decreases,  the  cost 
of  foundations  decreases  in  proportion.  The  use  of 
ribs  instead  of  slabs,  is  a  more  scientific  type  of 
construction  and  allows  the  strongest  supporting 
members  to  be  placed  exactly  where  required. 
Ribbed  concrete  arches  are  purely  a  product  of  this 
new  material  and  are  possible  in  concrete  only  when 
properly  reinforced  with  metal.  Concrete  ribbed 
bridges  are  built  mostly  in  the  form  of  arches, 
though  other  forms,  as  cantilevers,  have  also  been 
used  with  varying  degrees  of  success.  Many  bridges 
designed  as  arches  have  cantilever  action  also,  or 
when  the  rise  is  small  in  proportion  to  the  span, 
the  stresses  are  chiefly  the  result  of  bending,  and 
regardless  of  theory  the  span  acts  then  more  as  a 
beam  than  as  an  arch.  The  uncertainty  in  refer- 
ence to  cantilever  or  beam  action  of  arches  can  be 
removed  by  building  an  open  vertical  joint  between 
the  arches  over  the  piers,  the  presence  of  which 
will  positively  prevent  any  cantilever  action.  While 
such  a  joint  removes  a  serious  uncertainty  of  de- 
sign, it  is  very  doubtful  whether  or  not  this  expedi- 
ent is  desirable,  for  the  cantilever  action  frequently 
adds  as  much  strength  to  the  bridge  as  does  the 
arch  and  when  properly  designed  and  built  to  re- 
sist both  sets  of  stresses,  the  presence  of  cantilever 
action  adds  greatly  to  its  strength  and  permanence. 
The  Walnut  Lane  bridge  at  Philadelphia,  and 
the  Rocky  River  and  Piney  Creek  bridges  now  un- 
der construction,  illustrate  to  some  extent  the  sa\- 
ing  which  may  be  accomplished  by  the  use  of  ribbed 


144        CONCRETE   BRIDGES  AND   CULVERTS. 

in  place  of  slab  arches,  and  yet  all  of  these  three 
bridges  are  only  partially  ribbed.  They  each  con- 
sist of  a  pair  of  twin  arch  rings  separated  by  a 
distance  of  from  10  to  20  feet,  which  space  be- 
tween the  rings  is  spanned  by  simple  floor  con- 
struction. The  saving  in  the  arch  ring  by  this  ex- 
pedient is  from  25%  to  30%  of  the  cost  of  the  ring, 
which  saving  would  be  still  further  increased  by 
using  entire  ribbed  designs.  The  Luxemburg  stone 
arch  bridge  in  Germany  with  a  span  of  275  feet, 
and  completed  in  the  year  1903,  is  of  the  same  type. 
An  unusual  example  of  ribbed  arch  design  pre- 
pared by  Mr.  Turner  of  Minneapolis,  is  shown  in 
Figure  27.  It  is  one  of  several  designs  submitted 
for  the  Grand  Avenue  viaduct  in  Milwaukee.  The 
main  compression  members  are  octagonal  and  are 
hooped. 

The  use  of  ribs  instead  of  slabs  makes  it  possible 
to  place  members  of  the  proper  strength  where  re- 
quired, as  for  example  under  lines  of  street  railway 
track,  where  heavier  ribs  are  usually  required  than 
under  other  parts  of  the  roadway.  Sidewalks  may 
be  bracketed  from  the  outer  ribs  and  properly  tied 
into  or  across  the  floor,  and  the  whole  design  exe- 
cuted in  a  more  scientific  and  economical  manner. 

The  principal  objection  to  the  use  of  ribs  is  the 
extra  cost  of  the  required  wooden  forms,  which  of 
course  is  much  greater  than  for  plain  curved  slabs. 
Notwithstanding  this  objection,  important  concrete 
arches  of  the  future  will  possibly  be  built  with 
ribs,  particularly  when  the  proportion  of  the  rise 
to  span  is  large. 


REINFORCED    CONCRETE    ARCH   BRIDGES.    145 

Intrados  Form. 

A  low  flat  opening  is  the  best  form  for  the  pas- 
sage of  water.  A  rectangular  opening  for  culverts 
with  the  height  greater  than  the  width,  will  cost 
less  than  when  the  width  is  the  greater  of  the  two 
dimensions.  This  is  clearly  shown  by  the  culvert 
design  given  in  Tables  VII,  VIII,  IX  and  X  of 
Part  IV,  but  the  decreased  cost  is  secured  at  the 
expense  of  efficiency. 

Intrados  forms  should  be  as  nearly  as  possible  ex- 
act mathematical  curves,  but  if  these  cannot  be 
secured,  they  should  then  approach  so  nearly  to  the 
exact  curves  that  the  lack  of  regularity  may  not  be 
detected  by  the  eye.  Three  and  five  centered  flat 
arches  as  approximation  to  the  ellipse,  are  usually 
unsatisfactory  because  the  breaks  in  the  curve  can 
be  detected.  If  a  flat  ellipse  is  desired,  the  curve 
should  be  an  exact  ellipse  and  not  an  approxima- 
tion. Ellipses  which  are  too  flat  are  not  artistic. 
A  rise  of  from  one-fourth  to  one-sixth  of  the  span 
will  give  a  better  appearance.  Natural  conditions 
or  grade  lines  will  frequently  prevent  even  this 
amount  of  rise,  and  it  must  then  be  determined  by 
stability  requirements,  which  should  not  be  less 
than  from  one-eighth  to  one-tenth  of  the  span.  The 
steel  arches  of  the  bridge  across  the  Mississippi 
River  at  St.  Louis  have  a  rise  of  one-eleventh  of 
the  span  and  there  is  at  Steyr,  Austria,  a  reinforced 
concrete  bridge  of  139-foot  span,  the  rise  of  which 
is  only  one-sixteenth  of  the  opening. 

Earth  filling  in  the  haunches  tends  to  make  the 


146        CONCRETE  BRIDGES  AND   CULVERTS. 

line  of  pressure  approach  the  form  of  an  ellipse, 
while  the  uniform  loads  including  the  weight  of 
arch  ring,,  filling  above  the  extrados,  pavement  and 
full  live  load  tends  to  depress  the  line  of  pressure 
to  the  approximate  form  of  a  parabola.  The  com- 
bined effect  of  these  two  tendencies  is  to  produce 
a  curve  approximating  a  circular  segment.  The 
resulting  curve  will  lie  nearer  to  the  ellipse  or  to 
the  parabola,  according  as  the  effect  of  haunch  fill- 
ing or  uniform  load  predominates. 

The  trial  method  of  determining  the  intrados 
curve  is  no  longer  necessary,  for  a  direct  method 
has  been  given.  Under  the  head  of  ''Theory  of 
Arches",  a  method  has  been  explained  for  deter- 
mining the  amount  of  crown  thrust  by  dividing  the 
center  bending  moment  by  the  rise.  The  simple 
beam  moment  at  any  other  point  is  equal  to  the 
crown  thrust  or  pole  distance  H  multiplied  by  the 
vertical  ordinate  in  the  funicular  polygon,  which  is 
the  intercept  between  the  closing  line  and  the  pres- 
sure curve.  Therefore,  dividing  this  bending  mo- 
ment by  the  crown  thrust  or  pole  distance,  gives 
the  proper  ordinate  or  rise  for  the  center  line  of  the 
arch  at  the  point  considered.  This  method  makes 
it  possible,  after  having  first  assumed  the  approx- 
imate form,  to  determine  directly  without  trial,  the 
exact  intrados  curve  for  uniform  loading.  When 
the  exact  linear  arch  has  been  found,  the  bridge  will 
present  a  better  appearance  if  a  regular  curve  be 
drawn,  such  as  a  segment  or  ellipse,  even  though 
the  use  of  a  regular  curve  makes  the  arch  some- 


REINFORCED    CONCRETE    ARCH   BRIDGES.    147 

what  thicker  in  certain  parts  than  is  required. 
After  having  drawn  the  correct  linear  arch,  the 
thickness  of  the  ring  for  uniform  loads  should  be 
proportioned  directly  to  the  thrusts. 

The  computations  are  much  simplified  if  the 
curve  be  considered  a  parabola,  and  this  assumption 
is  approximately  true  when  the  rise  is  small  in 
comparison  with  the  span.  Parabolic  and  seg- 
mental  arches  require  little  metal  reinforcing,  while 
elliptical  and  other  flat  arches  may  require  a 
greater  amount. 

Some  designers  prefer  to  use  an  intrados  curve, 
lying  half  way  between  a  segment  and  an  ellipse 
and  found  by  bisecting  the  vertical  intercepts  be- 
tween these  two  latter  curves.  Mr.  Burr's  Potomac 
Memorial  Design  No.  3  has  an  elliptical  intrados, 
with  a  rise  of  one-fourth  the  span,  and  a  segmental 
extrados. 

Spandrels. 

The  principles  already  given  for  the  spandrel  de- 
sign of  solid  concrete  arches,  apply  also  to  arches 
of  reinforced  concrete.  If  side  spandrel  walls  are 
used,  provision  should  be  made  for  expansion  or 
these  side  walls  will  crack.  A  dovetailed  expan- 
sion joint  is  the  most  satisfactory  one,  for  sufficient 
space  can  be  allowed  in  it  for  expansion,  while  the 
two  wall  sections  are  held  securely  together.  If 
an  expansion  joint  is  not  provided,  an  open  crack 
is  liable  to  develop  between  the  spandrel  wall  and 
the  arch,  and  if  an  effort  be  made  to  prevent  such 
an  opening  by  clamping  the  spandrel  with  metal 


148        CONCRETE   BRIDGES   AND   CULVERTS.     ' 

ties  to  the  arch  ring,  the  stress  in  the  arch  then 
becomes  indeterminate,  as  a  portion  of  the  load 
will  be  carried  by  the  arch  action  of  the  spandrel 
wall. 

Joints  in  continuous  walls  should  occur  at  in- 
tervals not  exceeding  20  to  25  feet.  It  has  been 
found  by  experience  that  temperature  cracks  occur 
in  solid  walls  at  about  these  intervals  and  if  artifi- 
cial joints  be  formed,  the  developing  of  unsightly 
and  irregular  cracks  will  be  avoided. 

All  exposed  flat  concrete  surfaces  should  be  pan- 
eled to  avoid  monotony.  It  is  difficult  to  build 
plain  surfaces  perfectly  straight  or  plumb,  and  the 
use  of  panels  with  pilasters  and  belt  courses  assists 
to  conceal  irregularities  and  imperfections  in  flat 
surfaces,  that  otherwise  might  be  quite  apparent. 

Open  spandrel  arches  in  the  haunches  produce  a 
light  and  artistic  appearance,  but  they  are  not  prac- 
ticable for  flat  arches. 

Spandrel  walls  may  be  built  either  as  curtains  to 
obscure  the  open  chamber  framing,  or  as  retaining 
walls  to  support  earth  filling.  As  retaining  walls 
they  may  be  built  either  as  solid  gravity  walls,  or 
as  lighter  reinforced  walls  with  counterforts.  In 
any  case  it  is  better  that  the  centers  be  removed 
and  the  arch  allowed  to  settle  before  building  the 
spandrel  walls. 

Piers  and  Abutments. 

On  the  stability  of  the  foundations,  the  strength 
of  the  whole  superstructure  depends.  The  piers 
and  abutments  include  all  of  the  structure  from 


REINFORCED    CONCRETE    ARCH   BRIDGES.    149 

the  ground  up  to  the  point  of  rupture.  The  total 
angle  included  between  normals  to  the  points  of 
rupture,  never  exceeds  120  degrees  and  is  usually 
from  90  to  110  degrees,  the  real  theory  of  arches 
applying  only  to  material  between  these  limits.  The 
part  below  the  points  of  rupture  must  be  designed 
in  connection  with  the  substructure. 

The  greatest  economy  in  the  design  of  abutments 
is  secured  by  using  low  springs.  If  higher  springs 
are  desired,  they  can  be  secured  by  false  side  walls 
as  explained  and  illustrated  in  Part  I.  Great  sav- 
ing can  be  effected  in  high  abutments  by  coring 
out  the  rear  and  transferring  the  thrust  to  the 
soil  through  vertical  walls  bearing  on  a  foundation 
slab  of  reinforced  concrete.  Abutment  wings  may 
be  built  as  cantilevers  from  the  arch,  extending 
into  the  embankment  only  far  enough  to  hold  the 
slope.  They  contain  much  less  masonry  than  the 
old  style  of  gravity  retaining  wing  walls.  Cantilever 
wing  walls  should  be  tied  together  with  rods  be- 
neath the  roadway,  to  resist  the  outward  thrust 
of  filling.  This  method  was  adopted  in  the  Topeka 
bridge. 

The  recent  failure  of  the  Peoria  bridge  over  the 
Illinois  River,  has  called  attention  to  the  need  of 
having  absolutely  secure  foundations.  The  Peoria 
bridge  was  destroyed,  not  because  of  any  lack  in 
the  design  of  the  superstructure,  but  because  of  the 
undermining  of  its  foundations. 

Flaring  gravity  wing  walls  are  more  economical 
than  straight  ones  of  the  same  type  and  better 


150        CONCRETE   BRIDGES  AND   CULVERTS. 

direct  water  to  the  opening,  but  straight  wings 
usually  present  a  better  appearance. 

River  piers  require  cut-waters  at  the  upper  end 
which  should  be  capped  with  stone  or  steel,  well 
anchored  into  the  masonry. 

Some  bridge  piers  have  been  given  a  different 
batter  on  the  two  sides  for  resisting  the  unequal 
thrust  on  the  sides  from  spans  of  different  lengths. 
The  piers  must  have  sufficient  thickness  to  resist 
the  uneven  thrust  caused  by  full  live  loading  on 
one  span  and  no  live  load  on  the  other.  Piers  must 
be  designed,  not  by  empirical  rule,  but  according 
to  the  stresses  that  they  actually  have  to  resist. 

The  presence  of  reinforcing  rods  for  resisting 
temperature  stresses  in  piers,  is  desirable  though 
not  necessary.  Piers  are  usually  well  protected 
from  the  direct  rays  of  the  sun,  and  rods  are  more 
useful  to  unite  the  mass  into  a  solid  monolith  than 
for  resisting  temperature  stresses. 

The  design  of  piers  for  reinforced  concrete 
bridges  does  not  differ  greatly  from  the  design  of 
piers  for  masonry  bridges,  and  most  of  the  discus- 
sion of  this  subject  for  Concrete  Bridges,  applies 
equally  here. 

Cost  of  Reinforced  Concrete  Bridges. 

There  are  numerous  considerations  that  affect 
the  cost  of  reinforced  concrete  bridges,  among  which 
are  the  nature  of  the  soil,  the  nearness  or  accessi- 
bility of  materials,  presence  or  absence  of  switch- 
ing facilities,  the  design  of  the  bridge  whether  solid 
filled  or  open  spandrel,  the  height,  width,  finish, 


REINFORCED   CONCRETE   ARCH    BRIDGES.    151 

paving,  wings,  etc.  They  will,  however,  rarely  if 
ever  cost  more  than  bridges  of  solid  concrete.  An 
original  formula  for  the  cost  of  solid  concrete 
bridges  has  been  given  in  Part  I,  but  for  convenience 
it  is  repeated  here.  It  is  as  follows  :  — 


100 

Where  C  is  the  cost  of  the  bridge  in  dollars  per 
square  foot  of  roadway, 

W,  the  total  width  of  deck  in  feet, 

II,  the  height  of  deck  above  valley  or  river  bottom, 
and 

F,  a  variable  factor  the  value  of  which  is  as  given 
below, 

The  function  HW,  or  the  product  of  height  by 
width,  is  the  cross-sectional  area,  and  may 
be  represented  by  the  letter  A.  Factors  F, 
are  for  bridges  with  solid  slab  arches,  while 
factors  F'  are  for  bridges  writh  partial  slabs, 
like  the  Walnut  Lane  bridge  at  Philadelphia, 
or  the  Rocky  River  bridge  at  Cleveland. 

Values  of  Factors  F,  and  F'. 

When  A  is     200,  then  F  is  1.5 

500,  "  1.0 

1000,  "'  M 

1500,  "  .48 

2000,  .42 

2500,  .36 

3000,  .32 

3500,  "  .285 


152        CONCRETE   BRIDGES  AND   CULVERTS. 

When  A  is  4000,  then  F  is  .262  and  F'  is  .96 

5000,  "  .224  "  .95 

6000,  "  .200  .94 

7000,  .180  "  .93 

8000,  "  .164  "  .92 

9000,  "  .152  "  .91 

10000,  "  .141  "  .88 

11000,.  "  .133  "  .86 

12000,  "  .125  "  .85 

This  formula  will  give  costs  that  should  rarely  if 
ever  be  exceeded.  Generally,  however,  econom- 
ically designed  reinforced  concrete  bridges  should 
cost  from  25%  to  50%  less  than  the  costs  given  by 
the  formula  for  bridges  in  solid  concrete.  In  a  few 
cases,  the  cost  of  bridges  in  reinforced  concrete 
have  exceeded  that  given  by  the  formula,  but  these 
cases  are  rare.  Where  the  height  does  not  exceed 
15  to  20  feet,  the  cost  will  usually  vary  from  $2.00 
to  $4.00  per  square  foot  of  floor  surface,  while  for 
greater  heights  it  may  be  twice  these  amounts. 

The  total  cost,  as  well  as  the  cost  per  square  foot 
of  deck  for  a  miscellaneous  lot  of  reinforced  con- 
crete bridges  is  given  in  Table  No.  II.  The  square 
foot  cost  is  based  upon  the  total  length  of  bridge 
over  parapets  or  foundations,  and  not  upon  the 
length  of  opening.  If  based  on  the  latter  length, 
the  costs  per  square  foot  would  then  be  greater. 

The  cost  of  IS  concrete  arch  highway  bridges, 
built  by  the  city  of  Philadelphia,  is  reported  in 
Engineering  Record  January  23,  1909.  The  report 
states  that  the  bridges  were  mostly  single  span  with 


REINFORCED    CONCRETE   ARCH   BRIDGES.    153 

ornamental  balustrade,  washed  granolithic  surfaces 
and  paved  decks.  The  costs  based  upon  the  total 
length  of  bridge  vary  from  $1.73  to  $7.39  per  square 
foot,  or  an  average  of  $3.50  per  square  foot,  while 
the  costs  based  upon  the  width  multiplied  by  the 
clear  length  of  opening  vary  from  $3.10  to  $9.74,  or 
an  average  of  $6.25  per  square  foot.  The  total  cost 
based  upon  the  yardage  of  concrete  in  the  structure 
varies  from  $8.50  to  $11.25  per  cubic  yard.  The 
report  states  further  that  if  large  spalls  or  stones 
were  embedded  in  the  concrete  to  save  cement  and 
mixing,  the  cost  would  then  be  reduced  by  about 
20%. 

Compared  with  steel,  reinforced  concrete  bridges 
usually  cost  about  the  same  as  steel  bridges  with 
solid  floors.  The  report  referred  to  above  states 
that  those  built  in  Philadelphia  proved  to  be  cheaper 
in  first  cost  than  plate  girder  bridges  by  about 
25%,  but  if  maintenance  expense  is  considered,  the 
saving  is  still  greater. 

Comparative  estimates  for  the  Memorial  Bridge 
at  Washington,  one  design  for  which  is  given  in  the 
frontispiece,  showed  that  the  reinforced  concrete 
designs  cost  45%  more  than  corresponding  designs 
in  steel. 

A  bridge  over  the  Hudson  River  at  Sandy  Hill, 
N.  Y.,  consisting  of  15  ribbed  arch  spans  of  60  feet 
each,  cost  only  $2.30  per  square  foot  and  a  steel 
bridge  for  the  same  loads  w^ould  have  cost  as  much. 

Bids  received  for  a  bridge  over  the  Mississippi 
River  at  Fort  Snelling  Minn.,  consisting  of  two  arch 


154        CONCRETE  BRIDGES  AND   CULVERTS. 

spans  350  feet  in  length  each,  showed  that  the 
bridge  could  be  built  in  either  steel  or  reinforced 
concrete  at  about  the  same  cost. 

A  concrete  design  for  the  Richmond  trestle  shown 
in  Figure  40  is  reported  to  have  been  accepted  in 
preference  to  steel,  simply  because  it  was  the 
cheaper. 

Estimating. 

It  is  customary  to  estimate  the  total  cost  of  floor 
slabs,  including  concrete,  metal  reinforcement  and 
forms,  at  25  cents  per  square  foot  of  floor  for  the 
slab  only.  This  figure  is  made  up  as  follows : — 

Concrete,    6    inches    12  cents 

Metal     5  cents 

Wood  forms   8  cents 

Total    25  cents 

The  cost  of  forms  varies  considerably,  and  for 
floor  slabs  may  cost  from  8  to  20  cents  per  square 
foot  of  floor.  If  the  slabs  are  estimated  separately, 
then  it  is  necessary  to  estimate  also  the  cost  of 
floor  beams  and  spandrel  columns.  It  is  usual  to 
estimate  the  cost  of  forms  for  beams  and  columns 
of  ordinary  size,  not  exceeding  about  one  and  a 
half  foot  in  cross-section,  at  50  cents  per  lineal 
foot.  To  this  must  be  added  the  cost  of  the  con- 
crete and  steel  in  the  member.  The  total  cost  per 
lineal  foot  of  girder  or  columns  would  then  be  as 
follows : — 

Concrete  1  cu.  foot 25  cents 

Steel    15  cents 

Forms 50  cents 

Total  .  90  cents 


REINFORCED    CONCRETE   ARCH   BRIDGES.    155 


TABLE  II 

APPROXIMATE  ESTIMATING  PRICES 


Price  delivered. 

Price  in  Place. 

Earth  filling.  .  . 

$0  50  to  $1  00  per  yd 

Excavating,  ordinary.  .  . 

50  cu  ft. 

"         under  water  (including  cost 
of  cofferdam)  .  .  . 

4  00  cu  ft. 

Wood  piling  

35  lin  ft 

Sheet  piling  . 

40  00  per  M. 

Concrete  piling 

1  25  per  ft. 

Concrete  in  foundations  . 

6  00  "   yd. 

"        in  arch  rings 

8.00  "    " 

including  steel  reinforcement  .  .  . 

12.00  "    " 

Concrete  including  steel  reinforcement 
and  centers. 

18  00  "    " 

Steel  reinforcement,  riveted  work  
"    rods,  plain 

70.  00  per  ton 
30  00  "    " 

"    patented  rods  

50.00  "    " 

Brick,  common    . 

$6  00  to  $10  00  per  M 

20  00  per  M. 

"    face. 

30  00  "    " 

45  00  "    " 

"    moulded  
"    enameled  

50.00  "    " 
70.00  "    " 

70.00  "    " 
100.00  "    " 

Concrete  blocks,  10  inches  thick  
Sand  

.25cu.  ft. 
75  to  1  25   "    yd 

.SOcu.ft. 

Gravel.  . 

1  25  "     " 

Cement,  Portland  
"       non-staining.  . 

1  .  35  per  barrel 
3  25  " 

Crushed  limestone 

1  20  per  yd 

"        granite 

3  00  to  3  50  "    " 

Bedford  limestone.  . 

1  30  per  ft 

1  CO  per  ft. 

Carthage  limestone.  .  .  . 

2  00  "    " 

2  £0  "    " 

Kasota  or  Mankato  stone  
Granite  

2.50  "    " 
2  50  to  3  00  "    " 

2.80  "    " 
3  SO  "    " 

Bedford  ashlar  facing,  4  to  8  inches  thick. 

1.00  sq.ft. 

Bedford  stone  carving  

4.00  "    " 

Concrete  floor  slabs  (  concrete,  steel,  forms) 

.25  "    " 

Concrete  girders  and  columns  (concrete, 
steel  and  forms)  .  .  . 

1  00  lin.  ft. 

Concrete  columns,  spiral  wound  

1.70  "    " 

156        CONCRETE  BRIDGES  AND   CULVERTS. 

TABLE  II— Continued 

APPROXIMATE  ESTIMATING  PRICES 


Price  delivered. 


Price  in  Place. 


Bridge  pavements,  wood  block 

"  "  granolithic  walks. .  . 

"  "  brick 

asphalt 

"  stone  block 

"  "  granite  block 

Railing,  three  lines  pipe 

"      plain  iron  lattice 

"      fancy  iron  lattice 

"      artificial  stone 

Balusters,  turned  Bedford  stone 

Hand  rail  and  base  rail 

Stone  coping 

Intermediate  rail  posts 

End  newels 

Lamp  posts 

Trolley  poles 

Lumber  in  cofferdams 

"      "    arch  centers 

"      "    forms 

Beam  and  column  forms 

Metal  lath  and  plaster,  interior 

"      "        "        "        exterior 

Expanded  metal  No.  10,  4-inch  mesh. . . 

"    light 

Nails  and  spikes 

Tar  paper 

Toch  Bros,  waterproof  paint,  No.  10. . .' 
Bay  State  coating  (for  concrete  surfaces) 


$22.00 


.035  per  sq.ft. 
.02     "       " 


$1.50sq.  yd. 
1.50  "  " 
2.50  "  " 
3.50  "  " 
3.00  "  " 
4.50  "  " 
1.00  per  ft. 
2.00  "  " 
5.00  "  " 
6.00  "  " 
1.00  each 

.60  per  ft. 
2.00  "    " 
8. 00  to  12. 00 each 
10.00  "100.00  " 
100.00  " 
75.00  " 
40. 00  per  M. 
32.00  "    " 
.08  sq.  ft. 
.SOlin.  ft. 
.50  per  sq.yd. 


.03  perlb. 
.OOSper  sq.ft. 
1.25     "gal. 

.02      "sq.ft. 


20.00 
15.00 


REINFORCED    CONCRETE   ARCH   BRIDGES.    157 

If  the  girder  or  column  is  larger  than  12  inches 
square,  the  cost  of  the  concrete  will  then  increase 
in  proportion  to  its  area. 

In  making  up  a  tender  on  a  prospective  contract, 
it  is  necessary  that  all  items  of  expense  be  included 
and  provided  for.  Some  of  the  extra  expense  items, 
that  are  not  included  in  the  regular  estimate,  are 
as  follows : — 

Superintendent. 

Foreman. 

Timekeeper. 

Traveling  Expenses. 

Bond.  Cost  is  1  per  cent,  on  amount  of  bond,  which  is 
usually  25  per  cent,  of  contract. 

Telephones. 

Watchmen. 

Fire  Insurance. 

Liability.    Cost  is  2*  to  3|  per  cent  of  amount  of  pay  roll. 

Permit  and  License. 

Water. 

Setting  out  survey. 

Rent  of,  or  depreciation  on  plant. 

Office  and  Storage  sheds. 

Material  tests. 

Models. 

Signal  lights. 

Pumping  and  Baling. 

Refilling  and  Leveling. 

Shoring. 

Removing  Rubbish. 

Incidentals. 

Surfacing. 

These  items  must  be  provided  for  and  the  amount 
of  profit  desired  added  to  the  total. 

The  approximate  estimating  prices  given  above, 
should  be  changed  to  suit  local  conditions  and  the 
varying  state  of  the  market.  Prices  of  material  and 
labor  change  according  to  location  and  time,  and 
prices  that  are  suitable  in  the  East  may  not  hold 


158        CONCRETE  BRIDGES  AND   CULVERTS. 


for  work  in  the  West  or  South.  The  greatest  care 
is  necessary  in  estimating  the  foundations,  for  the 
part  that  is  unseen  is  uncertain.  It  is  well  to  make 
unit  prices  for  a  greater  or  less  amount  of  founda- 
tions than  is  shown  on  the  plans,  for  frequently 
more  is  required  than  is  anticipated. 

Table  of  Approximate  Quantities. 

The  following  table  gives  the  approximate  quan- 
tities in  Reinforced  Concrete  Arch  Highway  Bridges 
for  clear  spans  varying  from  20  to  150  feet,  and  a 
clear  width  of  roadway  of  16  feet. 

They  have  solid  earth  filled  spandrels  with  rein- 
forced concrete  side  retaining  walls  and  the  rise  of 
arch  is  one-tenth  the  span. 

They  are  proportioned  for  a  live  load  of  200 
pounds  per  square  foot  on  the  roadway.  The  quan- 
tities of  material  in  the  abutments  are  only  approx- 
imate. 

TABLE  OF  APPROXIMATE  QUANTITIES. 


Steel,  Bars  12  in.  c.  c. 

Clear  Span 
in 
Feet. 

Crown 
Thickness 
in  Inches 

Concrete 
in  Arch, 
Cu.  Yds. 

Concrete  in 
Abutments, 
Cu.  Yds. 

Size. 

Area  in  Sq. 
Ins. 

20 

9 

2      x     M 

.50 

30 

89 

30 

11 

2      x     A 

.62 

45 

118 

40 

13 

2j^  x     £ 

.78 

63 

140 

50 

15 

2  ^  x     jHi 

.93 

89 

162 

60 

16.5 

3     x    A 

.94 

118 

205 

70 

18 

3      x     H 

1.13 

150 

240 

80 

19 

1.31 

186 

280 

90 

21 

3  iz  x    .i. 

1.53 

220 

320 

100 

22 

4    x    ys 

1.50 

265 

360 

110 

24 

4      x    A 

1.75 

312 

410 

120 

26 

1.69 

360 

460 

130 

28 

4  J^z  x    -fs 

1.97 

415 

515 

140 

30 

5x^ 

1.88 

475 

570 

150 

32 

5      x    A 

2.19 

540 

630 

REINFORCED    CONCRETE   ARCH   BRIDGES.    159 

Potomac  Memorial  Bridge  Design. 

This  is  one  of  several  designs  submitted  to  the 
United  States  Government  in  the  year  1900  for  a 
proposed  memorial  bridge  across  the  Potomac  River 
at  Washington.  It  has  a  clear  width  of  60  feet,  con- 
sisting of  a  40-foot  roadway  and  two  10-foot  side- 
walks. The  total  length  of  open  bridge  is  3,400 
feet.  It  has  one  deck  and  no  provision  for  car 
tracks.  There  are  six  segmental  reinforced  con- 
crete arch  spans  of  192  feet  clear  length  and  29 
feet  rise,  with  53  feet  clearance  underneath.  A 
double  leaf  trunnion  bascule  draw  span  is  centrally 
located  between  the  arch  spans,  having  a  clear  open- 
ing of  159  feet  and  a  distance  between  centers  of 
trunnions  of  170  feet.  The  Washington  approach 
consists  of  twelve  semicircular  reinforced  concrete 
arch  spans  of  60  feet  clear  length,  and  550  feet  of 
embankment,  while  the  Arlington  approach  has  fif- 
teen similar  spans  and  1,350  feet  of  embankment. 
The  entire  exterior  surface  is  shown  faced  with 
granite.  The  face  rings  for  main  spans  are  5  feet  6 
inches  deep  at  the  crown  and  9  feet  6  inches  at  the 
springs.  Each  main  span  has  five  concrete-steel 
arch  ribs  30  inches  deep  at  the  crown  and  7  feet  3 
inches  at  the  springs,  supporting  a  system  of  in- 
terior steel  columns  carrying  the  floor  beams.  Span- 
drel curtain  walls  with  expansion  joints  rest  upon 
the  arch  rings  and  are  faced  with  granite.  The 
design  shows  asphalt  <road  and  granolithic  walks 
laid  on  concrete  floor  arches  between  the  steel  floor 
beams.  The  estimated  cost  is  $3,680,000.  William 
II.  Burr,  engineer;  E.  P.  Casey,  architect. 


163 


REINFORCED    CONCRETE   ARCH   BRIDGES.    161 

Jamestown  Exposition  Bridge. 

This  bridge  was  built  in  1907  by  the  United  States 
Government  to  connect  the  outer  ends  of  two  piers. 
It  is  of  reinforced  concrete  and  has  a  clear  span 
of  151  feet,  with  a  20-foot  rise.  It  is  36  feet  wide 
and  is  for  pedestrians  only.  The  ascent  of  the  road- 
way is  made  by  means  of  a  series  of  steps  and  land- 
ings. It  has  two  reinforced  concrete  arch  ribs  car- 
rying the  roadway  on  four  longitudinal  walls. ^The 
abutments  are  cored  out  and  rest  on  piles/There 
are  26  plumb  piles  and  126  batter  piles'  under  each 
abutment.  It  was  designed  and  built  by  the  Sco- 
field  Company  of  Philadelphia. 

Franklin  Bridge,  Forest  Park,  St.  Louis. 

Forest  Park  has  a  very  interesting  concrete 
bridge  of  the  Melan  type,  known  as  Franklin 
Bridge.  It  has  a  span  of  60  feet,  a  total  width  of 
33  feet,  and  a  rise  of  15  feet.  It  has  a  24-foot  road- 
way and  one  6-foot  sidewalk,  with  a  total  length  of 
92  feet.  The  arch  ring  is  three-centered  and  varies 
in  thickness  from  11  inches  at  the  crown  to  30 
inches  at  the  springs.  At  the  four  corners  there 
are  ornamental  iron  lampposts  not  shown  in  the 
illustration.  Its  total  cost  was  $5,600.  The  Geisel 
Construction  Company  were  the  contractors  and 
John  Dean,  Engineer  for  the  Park  Department. 

Jefferson  Street  Bridge,  South  Bend,  Ind. 

The  bridge  across  the  St.  Joseph  River  with 
four  elliptical  arches  of  110-foot  span  each.  The 
piers  are  quite  elaborate  in  design,  being  carried 


162 


REINFORCED    CONCRETE   ARCH   BRIDGES.    163 

up  to  support  retreats  at  the  sidewalk,  and  there 
is  a  heavy  moulded  cornice  surmounted  with  an 
artistic  railing.  At  the  ends  are  steps  leading  down 
from  the  roadway  to  the  river.  The  lines  of  the 
structure  are  true  to  a  design  in  concrete,  and  there 
has  been  no  effort  made  to  imitate  stone.  The 
Concrete  Steel  Engineering  Company  of  New  York, 
were  engineers,  and  James  0.  Heyworth  of  Chi- 
cago, contractor.  A.  J.  Hammond,  City  Engineer 
of  South  Bend. 

Gary,  Indiana,  Bridge. 

Gary  is  the  home  of  the  new  steel  companies 
where  an  entirely  new  town  is  being  built.  The 
bridge  shown  is  quite  ornamental,  and  illustrates 
some  possibilities  for  single  spans.  The  face  of 
arch  and  spandrels  are  paneled,  and  the  wings  are 
curved  to  facilitate  approach.  At  either  end  of  the 
arch  are  pilasters  extending  up  to  the  cornice  and 
forming  in  the  balustrade,  pedestals  for  future  lamp 
standards.  The  bridge  spans  the  Calumet  River 
and  was  built  in  1908  by  Rudolph  S.  Blome  &  Co., 
of  Chicago. 

Como  Park  Foot  Bridge,  St.  Paul. 

The  Como  Park  Bridge  was  built  in  the  year 
1903  for  the  Twin  City  Rapid  Transit  Company  to 
carry  traffic  entering  Como  Park,  over  the  tracks 
of  the  street  railway  company.  The  bridge  has  a 
clear  span  of  50  feet,  a  roadway  of  15  feet  and  is 
built  on  the  Melan  system.  As  a  large  number  of 
passengers  leave  the  cars  at  the  bridge,  it  was 


164 


L 


165 


166        CONCRETE   BRIDGES  AND   CULVERTS. 

desirable  that  the  structure  should  have  a  neat  ap- 
pearance. In  order  to  avoid  form  marks  on  the 
exposed  surfaces  the  forms  were  covered  with  metal 
lath  and  neatly  plastered  before  placing  the  con- 
crete. The  length  between  centers  of  abutment 
piers  is  83  feet,  and  the  total  width  of  arch  is  17 
feet  2  inches.  It  has  a  rise  of  12  feet  6  inches,  and 
is  10  inches  thick  at  the  crown.  The  length  of  span 
openings  over  spandrels  and  abutments  is  12  feet, 
and  the  thickness  of  the  skewback  piers  is  2  feet. 
There  are  five  latticed  steel  Melan  arch  ribs  in  the 
concrete.  It  was  built  by  William  S.  Hewitt  &  Co., 
of  Minneapolis.  George  L.  Wilson  was  consulting 
engineer. 

Boulder-Faced  Bridge,  Washington. 
In  a  park  at  Washington,  D.  C.,  there  is  a  boulder- 
faced  arch  of  rustic  design  made  to  conform  with 
the  surroundings.  It  has  a  span  of  80  feet,  a  rise 
of  15  feet,  and  "a  clear  width  of  roadway  between 
parapets  of  23  feet.  The  entire  arch  ring  is  built  of 
concrete,  but  the  soffit  is  darkened  with  lampblack 
to  harmonize  with  the  boulder  facing.  The  boulders 
of  the  arch  ring  extend  down  below  the  soffit  sev- 
eral inches,  and  partly  obscure  the  concrete  arch 
soffit.  It  was  built  in  1901  at  a  cost  of  $17,500. 
W.  J.  Douglas,  Engineer. 

Grand  Rapids  Arch  Bridge. 

This  is  a  good  example  of  the  best  American 
practice  in  reinforced  concrete  arch  bridge  design. 
It  has  five  spans,  the  center  one  being  87  feet,  the 


REINFORCED    CONCRETE   ARCH   BRIDGES.    169 

two  adjoining  ones  83  feet,  and  the  two  end  spans 
79  feet.  It  has  a  clear  width  between  railings  of 
64  feet.  The  piers  have  moulded  concrete  cornices 
at  the  springs,  and  there  is  a  continuous  cornice 
supported  on  brackets  at  the  floor  level.  There 
are  retreats  in  the  sidewalk  above  the  piers,  and 
a  heavy  open  balustrade  with  seven  heavy  railing 
posts  in  each  span.  It  was  designed  by  William  F. 
Tubesing  under  the  direction  of  L.  "W.  Anderson, 
City  Engineer,  and  was  built  in  1904  by  J.  P. 
Rusche,  contractor,  of  Grand  Rapids,  Mich. 

Bridge  at  Venice,  California. 

At  the  little  town  of  Venice  in  lower  California, 
laid  out  with  numerous  canals  in  imitation  of  Itaf 
ian  Venice,  are  a  number  of  bridges  mostly  built 
of  concrete  with  features  of  unusual  design.  The 
town  being  on  the  sea  coast,  in  a  region  where 
flowers  and  foliage  abound,  has  probably  suggested 
the  ornamentation.  The  faces  of  the  arch  are  elab- 
orately decorated  with  festoons,  and  on  the  ends  of 
the  balustrade  are  grotesque  figures  of  sea  animals 
in  concrete,  the  size  of  which  may  be  estimated  by 
comparison  with  the  people  on  the  bridge. 

Garfield  Park  Bridge,  Chicago. 

The  illustration  shows  an  attractive  park  bridge 
built  in  the  year  1893  in  Garfield  Park.  The  open 
balustrade  with  the  heavy  circular  piers  together 
with  the  combination  of  rough  and  smooth  finish 
unite  to  produce  a  pleasing  appearance.  Medal- 
lions on  the  piers  have  monograms  with  the  park 


eg 


§8 


REINFORCED    CONCRETE   ARCH   BRIDGES.    173 

initials,  and  the  spandrels  are  paneled.  The  balus- 
trade posts  are  mounted  with  ornamental  urns.  The 
design  is  one  which  can  well  be  reproduced  in  con- 
crete with  either  cut  stone  or  moulded  concrete 
facing. 

Stein-Teufen  Bridge,  Switzerland. 

The  longest  concrete  arch  span  completed  is  at 
Stein,  Switzerland.  Its  total  length  is  550  feet,  and 
the  roadway,  32  feet  wide,  is  216  feet  above  the 
Sitter  River.  The  central  span  is  259  feet,  with  two 
approach  spans  33%  feet  long  at  the  Teufen  end, 
and  four  at  the  other  end.  The  central  piers  are 
heavily  reinforced  to  resist  unbalanced  thrusts  from 
the  adjoining  arches.  The  main  arch  rings  are  21% 
feet  wide  and  4  feet  thick  at  the  crown,  increasing 
to  the  springs,  and  reinforced  with  li/s-inch  round 
bars  from  10  to  18  inches  apart.  It  has  a  Telford 
pavement  and  2-foot  walks  on  concrete  slabs  sup- 
ported on  stringers  and  spandrel  columns.  The  con- 
crete balustrade  has  openings  3  feet  wide,  guarded 
with  embedded  bars.  It  was  designed  by  Professor 
Morsch,  and  cost  $80,000. 


174        CONCRETE   BRIDGES  AND   CULVERTS. 


TABLE  III 

LIST  OF  REINFORCED  CONCRETE  BRIDGES 


Number.  I 

PLACE. 

Over. 

-71 

1 

1 
6 

'2' 
2 
li 

1 
2 
1 
2 
1 
1 
1 
1 
1 
1 
1 
2 
2 

1 
1 
2 

1 
1 
5 
1 

2 
2 
2 
1 

• 
1 
2 
4 
3 
5 
1 
2 
1 
2 
3 

r£ 

"8 

•t 
J 

259 
33.5 
197 
184 
177 
175 
167 
164 
131 
160 
70 
151 
146 
145 
144 
139 
132 
125 
110 
97.5 
122 
120 
120 
100 
120 
118 
114 
110 
100 
90 
80 

no 
no 
no 

100 

no 
no 

90-110 
108 
104 
108 
96 
107 

5 

J 

! 
I 

550 
812 

£ 

•T3 

i| 

*£ 

w 

1 

1 
2 

3 
4 
5 

6 
7 

8 
0 

10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 

Stein,  Switzerland  

Fogaras-Kronstadt,  Hungary  .  . 
Decize,  France  
Pyrimont,  France  

Bormida,  Italy  
Chatellerault,  France  

Painesville,  Ohio.  ..'.'.  '.  '.  '.  '.  '.  '.  '. 
Jamestown,  Virginia. 

Sitter  River  

Loire  River  
Rhone  River  

Vienne  River  
Grand  River  

87 
15 

"is" 

25 

16.7 
15.7 
13.2 
71 

"26" 
18 
33.5 

22 

34" 
12 

21t> 
'lOO 

48 
14 

'  C.'  ' 
Seg.' 

443 
401 

'265 
219 

26 
68 

36 
19 
21 

22 
90 

36 

Playa  del  Key,  Cal  

Vermillion  River  .  . 

Wakeman,  Ohio  
Routo  Waidhofen,  Austria  
Steyr,  Austria  

8.5 
16.2 
18.9 
16.3 
14.6 
11.4 
15 
12 
11.4 
23 
18 
14.4 
9.6 
11.3 
13.3 
14.3 
23.5 
40 
11.5 
10 

165 
244 
693 

'ieo 

404 

.214 

'716 
« 

'222 
371 

19.7 

74 

40 

12.8 
17 
20 

64 

54 
11.8 
12 

10.5 
40 
41 

19 
24 

32 

"43" 
39 

.25 
30 

"56" 
16 

Seg. 
3C. 

Branch  Brook  Park,  Newark  .  . 
Topeka,  Kansas 

Kansas  River  

Yellowstone  River 
Jacaquas  River.  .  .  . 

Grand  River  
Ravine  
Pena  River  
Miami  River  

Niagara  River  .... 

St.  Joseph  River  '.  . 
White  River  

Route  Wildegg,  Switzerland  .. 
Yellowstone  Park  
Porto  Rico  

Lansing,  Michigan  
Lake  Park,  Milwaukee  
Portugal  
Third  St.,  Dayton,  Ohio  

Boulevard,  St.  Paul  
Green  Island  

Jefferson  St.,  South'Bend.  '.'.'.'. 
Emerichsville  Ind.  . 

'l4!6 
14 
14.4 
9.5 
11.7 

'i70 
240 

522 

50' 
16 
45 

55 

25 
21 

30 

3  C.' 

Morris  St.,  Indianapolis  

Huntington,  Indiana  
Buda  Pesth,4  Austria  

Canal  Dover,  Ohio.  ..'.'.'.'.'.  '.'.'.'. 

Danube  River  
Tuscarawas  River  . 

REINFORCED    CONCRETE   ARCH   BRIDGES.    175 


TABLE  III— Continued 

LIST  OF  REINFORCED  CONCRETE  BRIDGES 


Crown  Thickness 
in  Inches. 

1 

I 

02 

Distance  Apart. 

£ 

fi 

w 

0 

«' 
W 
1 

3 

1 

Engineer. 

References. 

B.C.,  Eng.-Con. 
N.,      "     News 
R.,              Record 

.d 

s 

i 

w 

Cost  Per  Sq.  Ft. 

1 

ll 

10 

g 

1909 

H. 

$80,000 

Morsch  

N.,  Aug.  5,  '09... 

1 
2 

3 

IS 

H 

4 

.... 

1907 

H. 

$42,400 

De  Mollius  

N.,  Apr.  2,  '08... 

Rib. 

$5.50 

5 

g 

21 

100° 

H 

7 

22 
18 

S7 

1899 

90S 

H. 
R   R 

35,000 

Leffler.  .  .  . 

N.,  Apr.  10,  '02  .  . 
R    Apr.  24   '09 

Rib. 

3.05 

8 
9 
10 

54 
'94' 

...  . 

1907 

906 

'Seoneid'Eng.'Co'.!! 
De  Palo  . 

N.,  July  26    '06 

'Rib! 
Rib 

11 
12 
13 

...  . 

1908 

H. 
H 

16,870 

Watson  

E.G.,  Feb.  24,  '09 

Rib. 
Rib 

3H. 
?  H 

3.66 

14 
15 

24 

'26' 
19 

£ 

36 
36 
36 

897 
895 
897 

H. 
H. 
H. 

'  84,000 
150,000 

Reynolds  
Keepers  &  Thacher 

'R'.,'  Aug.'  12',  "'65'.: 

R.,  Apr.  16,  '98  .  . 
N.,Apr.    2,  '96.. 

'4'!65 
5.40 

16 
17 
18 
19 
90 

7 

890 

H. 

?1 

24 
28 
91 

ix'ji' 

24 
30 

1904 
1901 

H. 
H. 

59,440 

Crittenden  
Judson  

N.,  Jan.  14,  '04  .  . 
R.,  Aug.   3,  '01  .  . 
N    Aug    1    '01 

'•MO 

22 
23 
24 

25 

32 

1902 
1904 
1901 
1906 

H. 
H. 
E.  R. 
H. 

31,000 
184,000 

Newton  Eng.  Co.  .  . 
Turner  

E.G.,  Mar.  17,  '09 
R.,  Nov.  25,  '05. 

R.,  Mar.'  4,  '06'.!' 

'Rib!  ' 

'4!is 

25 
26 
27 
28 
29 

•i 

ii 

ii 

ii 

^0 

** 

" 

" 

K 

Rib 

31 
¥> 

40 

e'x'ji' 

36 

1909 
900 

H. 
H. 

18,800 
102,070 

C.  A.  P.  Turner  .  .  . 

R.,  Apr.    3,  '09  .  . 
N.,  Dec.   6   '00 

2.12 
6.60 

33 
34 

38 

F,  R 

Hammond  

R.,  Feb.  16,  '01  .  . 

.... 

35 
36 

H. 

37 

H. 

38 

20 

4? 

901 

H. 

32,000 

Melan  

N.,  July  16,  '03 

3  77 

39 

21 
20 

a 

12 

907 
900 

H. 
H, 

Luten  

40 
41 

94 

•I9 

24 

in 

12 

905 

H. 

105,000 

Thacher  

R.,  Feb.    9,  '07.. 

^-—  - 

43 

176        CONCRETE  BRIDGES  AND   CULVERTS. 


TABLE  III— Continued 

LIST  OF  REINFORCED  CONCRETE  BRIDGES 


Number. 

PLACE. 

Over. 

No.  Span  . 

02 

*s 

1 

1 

% 

£ 

i 
1 

"c« 
1 

4 

^ 

55 

52 

40 
SO 

42.7 

7.5 

28 

18 
22 
54 

16 
56 

50 

54 

53 
16 
36 
26 

27 

45 

I 

Z 

3 

o 

44 
45 
46 
47 
48 
49 
50 
51 

52 

53 
54 
55 

56 
57 
58 
59 
60 
61 
62 
63 
64 
65 
66 
67 
68 
69 
70 
71 
72 

7^ 
75 

76 

78 
79 
80 
81 
82 

Canal  Dover,  Ohio  
Pelham  
"      Draw  Span  

Tuscarawas  River. 
Chester  Bay  

Passaic  River  
Wabash  River  .... 

Des  Moines  River.  . 

Hoosatonic  River  . 
Sangamon  River  .  . 

1 
(i 
1 
1 
1 
2 
2 
2 

3 

1 
2 

2 
1 
2 
1 

2 
2 
2 
12 
1 
2 
2 
2 
3 
1 
2 
2 
1 
5 
1 
2 
1 

3 
1 

8 

10 
1 
2 
1 

70 
105 
62 
108 
100 
95 
80 
75 

100 

100 
100 
93 
95 
90 
90 
86 
80 
74 
75-90 
88 
83 
76 
69 
88 
87 
83 
79 
85 
83.5 
81 
81 
80 

80 

77 

75 
75 
75 
73 

75 

10 
16.5 

'l2" 
15 

13 

T27.7 
23.9 
[20. 
10 
30 

11 
15.7 
11.5 
10 
9.3 
8 
22-25 

"9  .'5 

"8 
11 

8.5 
8.2 
8 
9.7 
15 

8 

7 

7 
11 
11 

14.7 

522 

807 

360 
686 

360 

124 
640 

'm 

620 

1200 

588 

317 
493 

144 

494 
107 
187 
130 

305 

30 
30 

20 

28 

24 
32 

15 
60 

"26" 
30 

tt 

45 
30 

i< 

18 
30 

18 
20 
16 
18 
18 

30 

'EL" 

3  C.' 
3C. 

3C.' 

5  CY 
Seg. 

Seg.' 
Seg. 

Paterson,  New  Jersey  
Wayne  St.,  Peru,  Indiana  

Sixth  Ave.,  Des  Moines,  Iowa.  . 

Stockbridge,  Mass  
Decatur,  Illinois  

Yorkton,  Indiana  .  

Cartersburg,  Indiana  
Washington  St.,  Dayton  

Waterville,  Ohio  '.'..... 

Main  Street,  Dayton  

it        i>           <i 

Miami  River  

Maumee  River.  .  . 
Miami  River  

Passaic  River.  .  .  . 
Grand  River  

Prospect  Avenue 

Paterson,  New  Jersey  
Grand  Rapids,  Mich.  

Seeley  St  Brooklyn 

New  Goshen  Ohio 

Sarajero,  Bosnia.  
Decorah,  Iowa  
Washington,  D.C  

Soissons  France 

Miljacka  
'  Rock  :  Creek.  '.'.'.'.'.'. 
Aisne  River  

Colfax  Ave.,  South  Bend  

'780 
257 

42 
19.5 

20" 

"is" 

21 

3C. 
5  C.' 

Pollasky,  California  
Kresno  Galicia  

San  Joaquin  River 

Hyde  Park-on-Hudson  

Crum  Elbow  Creek 

REINFORCED    CONCRETE   ARCH   BRIDGES.    177 


TABLE  III — Continued 

LIST  OF  REINFORCED  CONCRETE  BRIDGES 


Crown  Thickness 
in  Inches. 

gj 

A 
m 

Frame 
...._.. 

¥ 

71 
1 

I 

i 

1 
« 

O 

ri 

o 
#' 
K 
| 

& 

t 

Engineer. 

References. 

C.,  Cement 
N.,  Eng.  News 
R.,     "    Record 

_Q 

s 

W 

S 
£ 
& 

iis'o 

1 

» 

15 
24 

'28 
25 

21 
21 

9 
45 

'2i 
20 
11 
7 
17 
24 
20 

15 

18 

18 
36 

'24' 
6 

12 

23 
12 

6 
36 

6 

36' 

'36' 
36 

1905 
1908 

1907 
1905 

1901 

1895 
1907 

1905 
1907 
1905 

1908 
1903 

1897 
1904 

"H." 

Thacher  
Lindenthal  

R.,  Feb.    9,  '07.. 
R.,0ct.  31,  '08.. 

44 
45 

46 
47 
48 
49 
50 
51 

52 

53 
54 
55 
56 
57 
58 
59 
60 
61 
62 
63 
64 
65 
66 
67 
68 
69 
70 
71 
72 
73 
74 
75 

76 

77 

78 
79 
80 
81 
£2 

H. 
H. 

H. 

F.  B. 
R.(R. 

E  R. 

37,200 
36,900 

Wise  

R.,  Mar.   7,  '08  .  . 
N    Mar  29   '06 

1,475 
117,000 

Von  Emperger  .... 
Cunningham  

Luten  
Luten  

C.,  July,  '02  

N.,  Nov.  7,  '95  .  . 
N.,  Mar.  21,  '07  .  . 

1.58 
6.50 

N.,  May  11,  '05.. 

:*£  _  Frames  '-  Frames  *-\ 

H. 

E.  R. 
H. 

122,000 

Turner  

R.,  Mar.   2,  '07.. 

3.60 

4^00 
4.30 

'2!90 
4.65 
4.30 

4i95 
'3!  15 

'  77,000 
140,000 

Walker  
Turner  

Thacher.  '.'.'.  

R.,  Aug.  8,  '03.. 
N.,  May  19,  '04  .  . 

N.,  Mar.  16,  '99  .  . 
N.,  Dec.    1,  '04.. 

N.,'bec.'3ir'03^ 
R.,  Mar.  30,  '07  .  . 

Tubesing  

'Fort.  '......  
Murray  

19 
27 
18 
12 
18 
17 

12 

16 
18 

'if> 

134 

m 
'"ii" 

'"x" 

8 
18 
24 
12 
33 

36 

1903 
1906 
1897 
1906 
1901 

1903 
1901 

1906 
1905 

R.  R 
H. 

21,803 
33,900 
16,500 

'  'l7,5bo' 
'  48,000 

Luten  
Douglas  

Riboud  

R.,  Aug.ie,  '02. 
N.,  Aug.  14,  '02 

Rib. 
Rib. 

Marsh  Bridge  Co. 
Leonard  

R.,'  Feb.'  24,  '06  ! 

1897 

H. 

Concrete  Steel  Co. 

178    '  CONCRETE   BRIDGES  AND   CULVERTS. 


TABLE  III— Continued 

LIST  OF  REINFORCED  CONCRETE  BRIDGES 


1 

83 

84 
85 
86 
87 
88 
89 
DO 
91 

92 
93 

94 
9,5 

96 
97 
98 
9i) 
100 
101 
102 
103 
104 
105 
100 
107 
IOS 
10':) 

110 

111 

112 
113 
114 
115 
116 
117 
118 
119 
120 
121 
122 

PLACE. 

Over. 

i 

0 

& 

3 
2 

4 
5 
3 

'3 
3 
3 

7 

1 

2 
4 
2 
2 
1 
3 
3 
1 
11 
3 
7 
15 
1 
2 
7 
11 
1 
1 
18 
1 
1 
2 

2 
2 
1 

•    CO 

•8 

js 

75 
75 
70 
95 
74 
74 
74 
72 
72 

70 
70 
70 
70 
70 
70 
70 
70 
69 
66 
66 
62 
60 
60 
59 
54 
50 
50 
50 
50 
45 
45 
40 
43 
42 
40 
38 
42 
39 
35 
38 

& 
'A 

J 

I 

240 

565 
284 

284 

'586 

163 
300 
201 
240 
89 
242 
270 

845 
755 

1025 
92 
161 
446 
613 
83 

l6i9 
65 
150 

53 

"56 
82 
216 

1 

^ 

32" 

56" 
70 
60 

54" 
46 

33 

16 
26 
64 
32 
24 
14 
20 

52" 

35 
33 
16 
23 
23 
17 
25 
26 
45 
16 

20 
15 
6 
63 
16 

48 

1 

6 

C 

3 

o 

Par 
El. 
El. 
3C. 
3C. 

'  C.'  ' 
C. 

5  C.' 
3C. 
Par. 

3  C.' 

Se^ 

3  C.' 

Seg.' 
Seg. 

'  C.'  ' 

"Big  Four"  bridge  near  Terre 
Haute  

"is" 
12" 

9.5 
9.5 

"j,  2 

10 
14 
20 
7 
18 
10.5 
9 
7 

14 
12 
8.5 
15 
8.5 
8 
4 
12.5 
11 

12 
6.2 
5.7 
8.5 
6.8 
4 

"7.'e 

7.2 
6.5 
7 

24 

"26 

18 
18 

"20 

"19" 

45 
15 
24 
13 
14 
20 

"30 
32-40 

24 

"is" 

22 
22 

"22" 
12 

11 

"s 

'J7 

Wabash,  Indiana  
Mission  Ave.,  Spokane  
Olive  Ave.,  Spokane  
Meridian  St.,  Indianapolis  
Illinois  St.  
Northwestern  Ave.,  Indianapolis 
Derby  Conn. 

Charley  Creek  

Spokane  River.  .  . 
Fall  Creek  

Waterloo,  Iowa  ^  

Eden  Park,  Cincinnati  
Logansport,  Indiana  

Park  Drive  
Pine  Creek  

Trinidad,  Colorado  
Wabash,  Indiana  

Seventeenth  St.,  Boulder,  Col 

Miners  Ford  
Guaya  River  

Porto  Rico  
Boulevard  Bridge,  Philadelphia 
Jacksonville,  Florida  
Herkimer,  K  Y  

Sandy  Hill,  N.  Y."  '.•'.'.'.'.'.'.'.." 
Franklin  Bridge,  St.  Louis  
Lima,  Ohio  
Plainwell,  Michigan  
Maryborough,  Queensland  
ComoPark,  St.  Paul  
Atlantic  Highlands,  N.  J  
Glendoin,  Cal  
Forest  Park,  St.  Louis  
London,  Ohio  

Cruft  St.,  Indianapolis  
Oconomowoc,  Wisconsin  
Columbia  Park,  Lafavette.  .... 
Interlaken  Bridge,  Minneapolis 
Plainfield,  Indiana  

Chicago,  C.  &  E.  I.  Ry  .  .  .  .  '.'.'.'. 

R.  R.  Tracks  
W.  Canada  Creek  . 

Hudson  River.  .  .  . 
Park  Stream  

Kalamazoo  River  . 
Mary  River  
Tracks  
Grand  Ave  
San  Gabriel  River  . 
River  Tes  Feres  .  . 

Trim  Creek.  ".'..'... 

REINFORCED    CONCRETE   ARCH   BRIDGES.    179 


TABLE  III— Continued 

LIST  OF  REINFORCED  CONCRETE  BRIDGES 


Crown  Thickness 
in  Inches. 

1 

i 

ro 

"a'x'i" 
"i6"'i 

10"  I 

I 

1 

1 

1 

^ 
w 

S 

« 
ffi 

•O 

s 

/ 

Engineer. 

References. 

E.G.,  Eng.-Con. 
N.,       "      News 
R.,        '     Record 

a 

id 

t 

£ 

£ 
& 

1 

J 

1 

'l8 

'27' 
16 
16 

'14 

15 
14 
40 
14 
18 
14 
13 

"is" 

21 

ii 

20 
18 
18 
10 
10 

'ii' 

14 
9 

24 

'36 
36 

"8"' 

36 
12 
12 
18 
24 
12 
12 

'ii' 

'36' 
8 
21 
24 

36 

'(}' 

12 

12 

1900 
1900 

1902 

1895 
1905 
1905 
1905 

1906 
1907 
1901 

1903 
1902 

1906 
1897 
1907 
1903 
1896 
1904 
1896 

1902 
1907 

1905 

R.  R 
H. 

'  ii.'  ' 

H. 

R.  R. 
H. 

'H.' 

'  H.'  ' 
E.uR. 

H. 

E.  R. 
H. 

F.  B. 
H. 
E.  R. 

E/R. 
H. 

Duane  

83 
84 
85 
86 
87 
88 
89 
90 
91 

92 
93 
94 
95 
96 
97 
98 
99 
100 
101 
102 
103 
104 
105 
1C6 
107 
108 
109 
110 
111 
112 
113 
114 
115 
116 
117 
118 
19 
120 
21 
22 

Hilty 

55,000 

'  54,400 
50,900 

Mclntyre  
Ralston  
Jeup  
Jeup  
Concrete  Steel  Co.  . 

N.,  Dec.   5,  '07. 

'N.,'Apr.'ii,''6i" 
N.,  Apr.  11,  '01.. 

E.G.','  Mar.  '17,'  '07 
R.,  Feb.  13,  '04 
N.,  Oct.    3,  '95. 

'2':  65 
2.90 

2166 

4!  75 
3^40 

i&xii 

9"  I 

H 
m 

& 
&i 

""\y* 

"8"'l 

* 

Frame 

•  •  6;/  j- 

....... 

H 

54,000 

25,680 
149,900' 

77,000 
5,640 

'  '19,900 
75,000 

'  '12,600 

Concrete  Steel  Co.. 
Von  Emperger.  .  .  . 

Wells  
Hibbard  

R.,  Sept.  22,  '06.. 
R.,  Feb.  10,  '06. 

Kahn  
National  Bridge  Co. 
Luten  
Ju  son  

Con  crete  Steel  Co.  . 
Osborn  

N.,'  Aug.'  'i,'  ;oi  ;  '. 

R.,  Apr.  20,  '06  .  . 
E.G.,  Sept.  2,  '08  . 

Burr  
Dean  
Luten  
Courtright  
Brady  

MelanCon.'Co'..'!. 
Mercereau  

N.,  May    9,  '07  . 
R.,  Dec.  10,  '98  . 

N.,'May'l2,"'04^ 
R.,Nov.l7,  '00. 
N.,  Apr.  6,  '05  . 

2.15 

1.84 

'1^96 
5.30 

'4!31 

Luten  

N.,'  Oct.'  19,'  ''99.': 

10 

is 

14 
13 
26 

H 
5 

12 

'4 
6 

8 

1902 
1900 

1905 

H. 
H. 

R/R. 

Luten  
Hewett 

Luten  

6.55 

12,000 

E.c!,Sept.2,  '08  i 

PART  III. 

Highway  Beam  Bridges. 

Comparison  of  Arch  and  Beam.  The  advantages 
of  arch  bridges  have  already  been  described  in 
Part  I  of  this  book,  and  original  formulae  have 
been  given  from  which  the  approximate  cost  of 
concrete  bridges  may  be  determined.  One  of  the 
chief  merits  of  arch  bridges  is  that  when  properly 
designed,  they  may  be  made  beautiful  in  outline. 

Some  of  the  advantages  of  beam  bridges  are  as 
follows: — (1)  It  is  possible  in  a  beam  bridge  to 
locate  the  grade  of  the  bridge  floor  much  lower  and 
nearer  to  the  high  water  level  or  other  clearance 
line  than  can  be  done  when  an  arch  is  used;  (2) 
foundations  for  beam  bridges  may  be  built  on  soil 
that  is  more  or  less  yielding,  which  cannot  be  done 
with  arch  bridges,  unless  hinges  are  used  at  the 
center  and  spring.  The  lateral  thrust  of  arches  on 
soft  foundations  is  liable  to  cause  serious  injury  to 
the  structure,  while  the  corresponding  amount  of 
settlement  under  the  abutments  of  beam  bridges 
produces  no  injurious  effect. 

A  frequent  objection  to  the  use  of  beam  bridges 
is  that  they  are  not  susceptible  to  artistic  treatment. 
It  will  be  seen,  however,  by  referring  to  Figures  37, 
38  and  39,  that  beam  bridges  may  be  designed  that 
are  equally  pleasing  in  appearance  to  arch  bridges, 
and  for  many  locations  are  more  suitable. 

In  making  a  selection  between  an  arch  and  a 
beam  design,  the  chief  consideration  will  generally 

181 


HIGHWAY   BEAM   BRIDGES. 


183 


be  their  relative  cost.  The  cost  of  concrete  arch 
bridges  has  already  been  given  by  the  formulae 
referred  to  above,  and  for  the  purpose  of  compar- 
ison, the  costs  of  concrete  beam  bridges,  in  spans 
ranging  from  4  to  40  feet  in  length,  are  given  in 
the  tables  on  Figures  38  and  39.  The  estimated 
costs  of  these  beam  bridges  include  the  filling,  pave- 
ment and  two  lines  of  railing,  but  do  not  include 
lamps  or  other  purely  ornamental  features.  On 
Figure  38  is  given  also  a  table  of  approximate  costs 
for  concrete  abutments  of  various  heights,  which 
estimates  also  include  railing  and  pavement  to- 
gether with  earth  excavation  and  back  filling  in  the 
abutments.  These  estimates  will  enable  the  de- 
signer to  compare  the  relative  cost  of  arch  and 
beam  bridges,  and  to  select  the  form  which  he  finds 
most  economical. 

TABLE  IV 


SPAN 


2  ABUTMENTS 


Estimate 

Length 

Thick 

Rods 

Steel 
Lbs. 

Cone. 
Cu.  Yds. 

Cost 

Ft. 

In. 

In.  Sq.  In.  cc. 

4 

6 

K       10 

112 

1.5 

$  70 

6 

6 

%       10 

232 

2.2 

110 

8 

7.5 

X            8 

365 

3.7 

150 

10 

9 

%            7 

510 

5.5 

200 

]2 

11 

%            6H 

612 

8.1 

250 

11 

12.5 

74                  7 

970 

10  8 

310 

16 

14 

%           614 

1160 

13.9 

370 

18 

16 

%           5L/2 

1540 

17.7 

410 

20 

18 

%            5 

1880 

22.2 

510 

Height 

Cost 

4 

$  280 

5 

340 

6 

410 

7 

510 

8 

650 

9 

770 

10 

880 

11 

1030 

12 

1190 

Beam  Bridges.  Concrete  beam  bridges  have  been 
built  in  spans  up  to  70  feet  in  length,  but  they  are 
not  generally  economical  for  lengths  exceeding  35 
feet,  for  above  this  length  arch  bridges  will  cost 
the  least. 


HIGHWAY  BEAM   BRIDGES. 


185 


The  economical  lengths  and  forms  for  concrete 
beam  bridges  are  as  follows :  Simple  slabs  are  eco- 
nomical for  spans  up  to  12  feet.  Beam  bridges 
similar  to  Figures  37  and  39,  supported  on  parallel 
longitudinal  beams,  are  economical  for  spans  from 
12  to  25  feet  in  length,  while  above  25  feet  it  is 
economy  to  use  two  lines  of  heavy  side  beams  carry- 
ing light  cross  beams  supporting  the  floor  slab. 

To  determine  the  economic  span  length  to  use  in 
a  long  bridge  containing  several  intermediate  piers, 

TABLE  V 


Span 

Side  Beam 

Center  Beam 

Estimate 

Cone. 

Rods 

Cone.  1   Rods 

Cone. 

Steel 

Cost 

Ft. 

Ft.  In.Sq. 

Ft.  In.  Sq. 

Cu.  Yds. 

Lbs. 

8 

12x20 

2-  3£ 

12xlfi 

3-  k 

3.8 

656 

$  164 

10 

12x20 

2-  % 

12x18 

3-  M 

4.9 

850 

207 

12 

12x20 

3-  % 

12x20 

4-  % 

6.1 

1160 

256 

14 

12x20 

3-  %  » 

12x23 

4-  % 

7.3 

1360 

304 

16 

1HX21 

3-1 

12x27 

4-  % 

8.9 

1780 

360 

18 

14x22 

3-1 

14x28 

4-  78 

11.2 

2000 

420 

20 

14x25 

3-1H 

14xM2 

4-1 

13.3 

2550 

490 

22 

14x28 

3-1*8 

14x35 

4-1 

15.5 

2800 

545 

24 

14x31 

4  - 

14x39 

4-1H 

16.2 

3350 

603 

26 

14x34 

4  - 

14x42 

4-1*8 

20.7 

3620 

682 

28 

14x37 

5- 

14x46 

6-1 

23.8 

4-460 

775 

30 

16x38 

5  - 

16x46 

6-1 

28.2 

4770 

855 

32 

16x41 

6- 

16x50 

,6  -1H 

32.0 

5800 

960 

34 

16x44 

6-1 

16x54 

6-1*8 

35.7 

6200 

1090 

,  36 

16x48 

7-1 

16x57 

8-1 

39.8 

7000 

1140 

38 

16x52 

7-1 

18x58 

8-1 

45.5 

7450 

1244 

40 

16x56 

T-1H 

18x62 

8-1*8 

51.2 

9400 

1400 

the  rule  is  to  select  such  a  span  length  that  the  cost 
of  one  span  will  be  approximately  equal  to  the  cost 
of  a  pier. 

Methods  of  Design.  Single  span  concrete  bridges 
of  either  slab  or  beam  design  must  be  considered 
non-continuous,  but  for  a  series  of  spans  the  effect 
of  continuity  in  the  beams  may  be  considered.  To 
provide  for  this  continuity,  it  is  customary  to  pro- 


186        CONCRETE   BRIDGES  AND   CULVERTS. 

portion  the  beams  for  only  80%  of  the  maximum 
bending  moment.  The  floor  slabs  must  be  pro- 
tected from  injury  by  a  sufficient  depth  of  earth 
filling,  which  is  shown  12  inches  on  Figures  38  and 
39.  This  provides  depth  enough  for  bedding  ties 
of  street  railway  tracks.  A  suitable  pavement  or 
wearing  surface  may  be  laid  on  this  earth  filling 
which  may  be  renewed  as  required. 

It  is  permissible  and  good  practice  in  designing 
small  concrete  beams  which  are  united  by  slabs,  to 
consider  the  effect  of  a  portion  of  the  floor  slab 
and  to  proportion  the  beams  as  T  beams.  Large 
longitudinal  beams  carrying  floor  loads  directly  to 
the  piers,  should  be  proportioned  as  simple  beams 
without  considering  the  effect  of  the  adjoining  slab. 
They  will  then  have  additional  strength  due  to  the 
presence  of  such  slab. 

The  bridges  shown  in  Figures  38  and  39  are  de- 
signed for  total  loads  of  from  400  to  500  pounds 
per  square  foot  of  floor  surface.  It  is  customary 
to  provide  for  impact  either  by  adding  a  percentage 
to  the  live  load  or  by  using  a  factor  of  2  for  dead 
load  stresses,  and  a  corresponding  factor  of  4  for 
live  load  stresses. 

It  has  been  proven  by  numerous  experiments  that 
the  adhesion  of  concrete  to  metal  is  sufficiently 
great  so  no  additional  bond  is  required,  but  as 
voids  in  the  concrete  are  liable  to  occur  and  it  is 
difficult  to  always  secure  the  highest  grade  of  work- 
manship, it  is  desirable  to  use  rough  bars  with 
mechanical  bond.  As  provision  must  also  be  made 


HIGHWAY   BEAM   BRIDGES.  187 

for  shear  by  the  use  of  inclined  or  bent  rods  and 
stirrup  irons,  it  is  desirable  in  all  large  beams,  to 
use  reinforcing  bars  which  have  the  inclined  stir- 
rups or  shear  members  rigidly  connected  to  the 
main  tension  metal. 

In  all  bridges  where  appearance  is  any  consider- 
ation, the  railing  should  be  designed  with  care  so 
the  design  may  properly  harmonize  with  the  rest 
of  the  structure.  Generally  speaking,  the  balus- 
trade that  presents  the  best  appearance  on  a  con- 
crete bridge  is  one  composed  of  either  natural  or 
artificial  stone,  but  it  is  also  evident  (Figure  39) 
that  an  equally  artistic  effect  may  be  secured  with 
an  ornamental  metal  railing  and  stone  or  concrete 
posts  and  pedestals.  Open  balustrades  are  usually 
preferable  to  solid  ones,  not  only  because  they  are 
susceptible  to  more  artistic  treatment,  but  also  be- 
cause their  light  and  open  design  emphasize  by  con- 
trast the  solidity  and  strength  of  the  supporting 
structure  beneath  them.  Solid  balustrades  are  per- 
missible chiefly  for  through  bridges,  where  the  con- 
crete side  girders  standing  above  the  roadway  form 
a  sufficient  protection.  The  exposed  girder  surface 
may  then  be  paneled  or  otherwise  ornamented. 


S  w 


188 


PART  IV. 

Concrete  Culverts  and  Trestles. 

Since  the  introduction  of  reinforced  concrete  as  a 
building  material,  many  railroad  companies  are  re- 
building their  permanent  bridges  and  culverts  in 
concrete,  either  plain  or  reinforced.  The  use  of  re- 
inforced concrete  for  culvert  construction  has  be- 
come almost  general  with  the  raihoad  companies, 
while  the  building  of  trestles  in  this  material  is  grad- 
ually coming  into  favor.  Many  old  wooden  struc- 
tures, both  of  the  open  and  the  gravel  deck  types, 
are  being  repjaced  by  better  ones  of  concrete  ma- 
sonry7. Amor.g  the  railroad  companies  that  are 
using  reinforced  concrete  extensively  for  the  con- 
struction of  trestles  may  be  mentioned  the  Illinois 
Central,  the  Cleveland,  Cincinnati,  Chicago  &  St, 
Louis  (Big  Four),  and  other  branches  of  the  New 
York  Central  Railroac  system.  A  notable  concrete 
trestle  or  viaduct  that  has  attracted  much  attention 
is  the  one  recently  built  at  Richmond,  Virginia,  for 
the  Richmond  &  Chesapeake  Bay  Railroad  Com- 
pany. This  viaduct  is  2,800  feet  in  length,  and 
varies  in  height  from  18  feet  at  the  ends  to  70  feet 
near  the  middle,  and  is  shown  in  Figure  40.  At  At- 
lanta, Georgia,  there  is  a  reinforced  concrete  viaduct 
carrying  Nelson  street  over  the  tracks  of  the  South- 
ern Railroad.  It  contains  10  spans  of  various 
lengths  from  20  to  75  feet,  has  a  total  length  of  480 
feet,  and  is  shown  in  Figure  41,  The  main  line  of 
the  Big  Four  Railroad  is  carried  for  a  distance  of 

iS9 


190       CONCRETE  BRIDGES  AND   CULVERTS. 

1,200  feet  across  the  Lawrenceville  Bottoms  on  a 
reinforced  concrete  trestle  20  feet  in  height.  This 
entire  region  is  periodically  flooded  with  backwater 
from  the  Ohio  and  Miami  rivers,  making  it  neces- 


Fig.  41. 
NELSON  STREET  VIADUCT,   ATLANTA,  GEORGIA. 

sary  to  build,  not  only  this  road,  but  all  others  in 
the  vicinity  at  an  elevation  of  30  feet  above  low- 
water  level  of  the  Ohio  River. 

On  the  following  pages  are  designs  and  estimates 
for  about  1,000  railroad  culverts  and  trestles,  and 


CONCRETE    CULVERTS    AND    TRESTLES.      191 

the  estimated  costs  are  given  on  charts  shown  in 
Figures  46,  47  and  66. 

Tt  will  be  seen  that  the  trestle  designs  are  equally 
suitable  for  culverts,  and  may  be  adapted  for  that 
purpose  by  increasing  their  width  to  correspond 
with  the  depth  of  structure  below  the  base  of  rail, 
or  to  conform  to  the  depth  of  the  embankment. 
When  used  as  culverts,  abutment  wing  walls  must 
be  added  and  the  nature  of  the  foundation  soil  may 
be  such  as  to  require  culvert  pavement.  These 
modifications  in  the  trestle  estimates  may  easily  be 
made  either  for  one  or  more  openings,  and  adapted 
for  either  single  or  double  box  culverts. 

The  culvert  designs  are  shown  with  a  minimum 
depth  of  filling  of  not  less  than  3  feet  above  the  con- 
crete top.  This  depth  is  desirable  not  only  for  the 
purpose  of  distributing  the  live  load  from  the  engine 
and  train  Avheels,  but  also  for  the  purpose  of  form- 
ing a  cushion  to  absorb  and  distribute  the  shock 
and  impact  from  rapidly  moving  trains.  Trestle  de- 
signs G  and  H,  Figures  64-65,  are  shown  with  a 
3-foot  depth  of  filling.  It  frequently  occurs,  how- 
ever, that  thin  floors  are  necessary  and  only  suf- 
ficient depth  can  be  secured  for  the  usual  15  inches 
of  ballast.  This  arrangement  has  been  shown  in 
trestle  designs  A  to  F  inclusive.  (Figures  58  to  63.) 

Required  Size  of  Culvert  Opening. 

The  most  important  consideration  effecting  the 
final  cost  of  a  culvert  is  the  selection  of  its  form 
and  size.  It  frequently  occurs  that  structures  of 


192       CONCRETE   BRIDGES  AND   CULVERTS. 

too  large  a  size  and  excessive  cost  are  specified, 
when  smaller  ones  \vould  be  ample  to  carry  off  the 
greatest  rainfall. 

The  selection  of  the  proper  size  of  culvert  is  of 
much  greater  importance  than  any  consideration  of 
design.  If  a  culvert  costing  $10,000  be  specified, 
where  a  smaller  one  costing  only  $5,000  would  bo 
sufficient,  the  loss  by  such  an  error  would  evidently 
be  $5,000.  On  the  other  hand,  if  the  size  of  struc- 
ture as  specified  be  used,  the  engineer  may  by  care- 
ful estimating,  select  a  form  with  the  required  wa- 
terway, and  with  a  cost  of  only  $8,000.  The  saving 
in  this  case  is  only  $2,000,  whereas,  if  greater  care 
had  been  given  to  the  selection  of  the  proper  size, 
there  might  have  been  a  saving,  not  only  of  this 
$2,000,  but  of  $5,000  additional.  It  will  be  seen, 
therefore,  that  the  one  consideration  outweighing  all 
others  in  effecting  the  final  cost  is  the  selection  of 
a  structure  with  the  necessary  waterwray. 

In  the  State  of  Wyoming  there  are  four  bridges 
within  a  short  distance  of  each  other,  carrying  a 
road  over  the  same  stream.  The  last  of  these 
bridges  to  be  built  has  two  spans  65  feet  in  length, 
or  130  feet  extreme.  The  second  bridge  has  two  40- 
foot  spans,  and  is  SO  feet  in  length.  The  third  has 
a  single  CO-foot  span,  while  the  fourth  is  an  old  30- 
foot  wooden  truss,  which  has  for  fifty  years  proved 
itself  sufficient  to  meet  even  flood  conditions.  There 
are,  therefore,  in  close  proximity  to  each  other  four 
bridges  over  the  same  stream,  the  longest  of  which 
is  four  times  greater  than  the  shortest,  and  the  long- 


CONCRETE    CULVERTS   AND    TRESTLES.      193 

est  one  was  the  last  one  built.  After  selecting  a 
length  of  structure  four  times  greater  than  required, 
it  is  possible  that  the  engineer  may  have  spent  con- 
siderable time  and  thought  in  his  endeavor  to  build 
this  bridge  at  the  least  possible  cost,  and  may  have 
succeeded  in  saving  a  few  hundred  dollars  on  his 
original  estimate. 

A  bridge  130  feet  in  length  would  cost  approxi- 
mately $7,000,  while  a  30-foot  bridge  would  not  ex- 
ceed $1,500.  This  saving  is,  therefore,  only  a  frac- 
tion of  the  saving  that  might  have  been  effected, 
had  a  30-foot  bridge  been  used,  which  length  had 
proved  sufficient  for  half  a  century. 

The  most  reliable  data  on  which  to  base  the  size 
of  a  prospective  structure  is  the  high-water  level  of 
previous  years.  It  is  frequently  possible  to  obtain 
such  data  from  local  records,  or  to  determine  the 
size  from  that  of  other  bridges  passing  the  same 
flow  of  water  in  the  near  vicinity.  In  the  case  re- 
ferred to  above,  if  the  engineer,  before  building  the 
130-foot  bridge,  had  made  sufficient  inquiry,  he 
could  easily  have  learned  that  a  30-foot  span  had 
carried  the  entire  stream  discharge  for  fifty  years, 
and  was  therefore  large  enough  for  the  rainfall  of 
the  future. 

It  is  not  economy  to  provide  openings  of  sufficient 
size  to  carry  the  rainfall  of  freshets  or  cloudbursts 
that  may  not  occur  oftener  than  once  in  a  century. 
For  such  unusual  occurrences  it  is  better  to  make 
occasional  repairs  than  to  invest  additional  money 
in  larger  structures  than  may  ever  be  required. 


194        CONCRETE   BRIDGES   AND   CULVERTS. 

when  such  money  might  be  drawing  interest  to 
cover  the  cost  of  an  occasional  repair. 

Where  reliable  data  in  reference  to  the  maximum 
rainfall  cannot  be  obtained,  it  is  customary  for  the 
railroads  to  build  temporary  wooden  trestles  at  the 
proposed  bridge  or  culvert  site,  and  to  make  these 
trestles  unnecessarily  long,  so  there  will  be  no  doubt 
whatever  of  the  openings  being  large  enough.  These 
temporary  bridges  will  last  from  six  to  ten  years, 
and  during  this  period  careful  observations  of  the 
water  flow  may  be  made,  and  other  data  secured 
from  which  to  determine  the  necessary  culvert  area. 
As  the  cost  of  these  temporary  trestles  will  not  ex- 
ceed $10  per  lineal  foot  their  entire  cost  may  easily 
be  saved  by  selecting  the  minimum  required  size  for 
the  permanent  structure. 

Where  no  reliable  data  in  reference  to  the  volume 
of  water  is  obtainable,  the  culvert  area  may  be  com- 
puted approximately  by  a  empirical  rule  knowrn  as 
Meyer's  Formula,  which  is  as  follows:  —  The  Re- 


quired Culvert  Area=^  Drainage  area  in  acres  X  F, 

where  F  is  a  coefficient  varying  from  unity  for  flat 
country,  to  4  for  rolling  or  mountainous  country, 
from  which  rainfall  is  discharged  at  a  greater  ve- 
locity. The  proper  value  for  this  coefficient  for  any 
particular  location  must  be  selected  entirely  by  the 
judgment  of  the  engineer. 

Reinforced  Concrete  Box  Culverts. 

The  following  series  of  designs     for  single  and 
double  box,  reinforced  concrete  railroad  culverts,  in- 


CONCRETE    CULVERTS    AND    TRESTLES.     195 

eludes  between  800  and  900  separate  estimates,  and 
is  therefore  very  comprehensive  and  complete.  The 
charts  of  comparative  costs,  Figures  46  and  47,  show 
these  to  be  more  economical  than  any  other  form  of 
culvert,  excepting  perhaps  reinforced  concrete  oval 
culverts  of  the  form  shown  in  Figure  57.  While  arch 
culverts  of  this  latter  form  may  contain  less  ma- 
terial than  box  culverts  of  equal  area,  they  are  more 
difficult  to  build  because  of  their  curvature,  even 
though  collapsible  centers  be  used.  Several  large 
railroad  systems  in  America  are  now  using  arch  cul- 
verts of  this  general  form,  in  place  of  the  old  seg- 
mental  or  semicircular  types,  which  contain  more 
masonry  in  the  abutments  than  in  the  arch  wing. 

Loads.  There  is  much  uncertainty  in  reference 
to  the  amount  of  load  carried  by  the  cover  of  a  rail- 
road culvert.  The  amount  of  this  load  depends  to 
a  great  extent  on  the  depth  of  the  culvert  top  below 
the  base  of  rail.  The  greatest  load  occurs  when  the 
depth  of  filling  above  it  is  a  minimum,  for  then  the 
culvert  top  is  subjected  to  the  entire  load  from  the 
locomotive  wheels  and  their  impact.  On  the  con- 
trary, when  the  culvert  is  buried  beneath  a  deep 
embankment,  the  live  load  and  impact  is  so  distrib- 
uted and  dispersed  that  only  a  part  of  this  load  goes 
directly  to  the  culvert.  Various  writers  have  en- 
deavored to  show  that  these  loads  are  distributed 
crosswise  of  the  embankment,  and  slope  outward 
from  the  railroad  ties  at  the  rate  of  one  foot  hori- 
zontal for  every  two  feet  vertical.  The  pressure  on 
the  base  of  these  triangles  varies  from  zero  at  the 


196        CONCRETE   BRIDGES  AND   CULVERTS. 

outer  point  to  a  maximum  under  the  end  of  tie.  This 
assumption  is  only  an  approximation,  though  a  rea- 
sonable one.  Unfortunately,  however,  the  author  of 
this  hypothesis  assumes  that  the  earth  pressures 
slope  outward  at  each  side,  but  makes  no  provision 
for  similar  distribution  lengthwise  of  the  embank- 
ment. It  is  quite  evident  that  whatever  distribution 
of  loads  does  occur,  must  occur  equally  in  all  direc- 
tions, and  the  assumption  referred  to  above  is  there- 
fore incorrect. 

Where  a  culvert  has  a  small  depth  of  filling  above 
it,  the  entire  weight  of  such  filling  is  then  sup- 
ported by  the  culvert,  but  if  located  at  the  bottom 
of  a  high  embankment,  the  culvert  then  carries  only 
a  portion  of  the  live  load  above  it,  supporting  also 
a  portion  only  of  the  earth  embankment.  The 
amount  of  this  portion  depends  upon  the  nature  of 
the  embankment  material.  If  this  material  is  ce- 
mented well  together,  it  will  then  tend  to  support 
itself  by  acting  either  as  an  arch  or  beam,  and  there- 
by relieving  the  culvert  of  much  superimposed  load. 
The  most  reasonable  assumption  is  to  consider  that 
the  culvert  carries  the  weight  of  a  triangular  sec- 
tion of  the  embankment,  the  sides  of  which  slope 
outward  from  the  vertical  in  the  ratio  of  one  foot 
horizontal  to  two  feet  vertical.  If  the  embankment 
material  is  composed  of  clean  sand,  a  larger  propor- 
tion of  the  imposed  material  will  then  be  borne  by 
the  structure.  In  view  of  the  uncertainty  of  various 
conditions  effecting  the  amount  of  load  on  culvert 
tops,  it  has  been  determined  that  these  loads  can 


CONCRETE    CULVERTS    AND    TRESTLES.      197 

never  exceed  the  values  occurring  under  a  minimum 
depth  of  earth  filling. 

An  assumed  live  load  on  each  track  equivalent 
to  Cooper's  engine  load  E.  50,  spread  out  by  the  ties, 
rails  and  ballast,  produces  a  distributed  load  on  the 
culvert  top  of  1,100  pounds  per  square  foot.  To 
this  has  been  added  impact,  amounting  to  50% 
of  the  live  load,  or  550  pounds  per  square  foot. 
Adding  to  these  the  weight  of  ties,  rails,  ballast, 
earth  filling  and  concrete  in  the  culvert  top,  pro- 
duces a  total  load  of  from  2,100  pounds  per  square 
foot  for  small  culverts  with  thin  slabs,  to  2,400 
pounds  per  square  foot  for  larger  spans  with  a 
greater  thickness  of  concrete.  The  following  box 
culvert  tops  are  therefore  proportioned  for  total 
loads  of  from  2,100  to  2,400  pounds  per  square  foot. 

From  the  theory  of  horizontal  earth  pressure,  it 
is  known  that  the  thrust  per  square  foot  on  an  em- 
bedded vertical  surface  is  equal  to  one-third  of  the 
corresponding  horizontal  pressure  on  a  unit  of  area 
at  the  same  level.  This  condition  exists  wrhen  the 
embankment  is  composed  of  clean,  dry  sand  with  an 
angle  of  repose  of  about  30  degrees.  The  proper 
amount  of  pressure  to  assume  on  the  culvert  side  is 
therefore  from  700  to  800  pounds  per  square  foot, 
or  one-third  of  the  corresponding  roof  loads.  As 
the  sides  are,  however,  subjected  to  vertical  loading 
and  impact  from  moving  trains,  the  assumed  side 
pressure  has  been  taken  at  one-half  of  the  vertical, 
or  from  1,050  to  1,200  pounds  per  square  foot. 

On  account  of  the  liberal  provision  for  impact, 


198        CONCRETE   BRIDGES   AND   CULVERTS. 


amounting  to  50%  of  the  live  load,  high 
working  values  have  been  used  for  concrete  and 
metal  reinforcement.  A  reasonably  rich  concrete 
mixture,  such  as  1-3-5,  has  an  ultimate  crushing 
value  of  2,800  pounds  per  square  inch.  One-fourth 
this  amount,  or  700  pounds  per  square  inch,  is  there- 
fore assumed  as  a  working  unit  for  concrete,  an«l 
12,000  pounds  per  square  inch  as  a  working  unit 
for  reinforcing  steel. 

Economic  Length  for  Slabs  and  Beams.  There  is 
evidently  a  limit  where  economy  ceases  in  the  use 
of  flat  slabs  for  supporting  loads  in  bending,  and 
above  that  limit  the  economical  construction  is  a 
combination  of  beams  and  slabs.  For  the  purpose 
of  determining  these  economic  lengths,  a  slab  table 
(Table  No.  VI)  has  been  prepared,  giving  the  amount 
of  concrete  and  steel  and  the  estimated  cost  per 
square  foot  for  spans  varying  in  length  from  4  to 
24  feet,  and  total  imposed  loads  of  from  2,100  to 
2,400  pounds  per  square  foot. 

TABLE   VI 

REINFORCED  CONCRETE  SLABS— SIMPLE  SPANS 
TOTAL  LOADS  2100  TO  2400  LBS.  PER  SQUARE  FOOT. 


Span. 

Effective 
Depth. 

Total                                                             Cost  per 
Depth.                        Sq.  Bars.                     square  ft. 
Cents. 

4 
6 
8 
10 
12 
14 
16 
18 
20 
22 
24 

6 
9 
12 
15 
18 
21 
24 
28 
31 
34 
37 

7  .  5                  8.4  i 
10.5                   7s 
13.5                   "8 
17.0                1 
20  .  0                1 
23.0                 1 
28  .  0                1  M 
30  .  5                1  \i 
33  .5                1  M 
37.0                1M 
40.0                ll/i 

n.  7  }  2  in  apa 

rt.                30  .  6 
43  6 
56.0 
71.6 
85.7 
97.7 
110.2 
131.5 
146.5 
159.0 
170.0 

4 

CONCRETE    CULVERTS    AND    TRESTLES.      199 

A  corresponding  set  of  ten  tables  was  made  giv- 
ing the  amount  of  material  and  the  estimated  costs 
per  square  foot  for  a  combination  of  beam  and  slab 
construction,  with  spans  varying  from  6  to  30  feet 
in  length,  and  beams  spaced  from  6  to  18  feet  apart, 
on  centers.  The  cost  results  from  these  ten  tables 
are  given  on  the  chart,  Figure  42.  The  thickness 
of  slabs  and  beams  are  proportioned  so  the  stress 
at  the  outer  edge  will  not  exceed  700  pounds  per 
square  inch  from  dead,  live  and  impact  loads.  The 
thicknesses  were  determined  from  the  writer's  orig- 
inal formula 


where  M.  is  the  bending  moment  in  inch  pounds, 

d    the  distance  from  slab  top  to  center  of  ten- 

sion bar,  and 
K  a  variable  factor. 

It  is  advisable  to  neglect  the  effect  of  continuity 
in  proportioning  slabs,  even  though  a  considerable 
amount  doubtless  exists,  Avhich  would  reduce  the 
slab  thickness  by  about  20%.  Slab  thicknesses  are, 
therefore,  given,  as  required  for  non-continuous 
beams.  From  the  comparative  cost  chart,  Figure 
42,  the  following  conclusions  are  obtained.  For 
loads  of  from  2,100  to  2,400  pounds  per  square 
foot  :  — 

Simple  slabs  are  economical  for  clear  spans  up  to 
7  feet  in  length. 

Slabs  with  beams  6  feet  apart  are  economical  for 
spans  from  7  to  14  feet  in  length. 


200        CONCRETE   BRIDGES  AND   CULVERTS. 


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Various  Beam  Spacing  also  Cost 
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Total  loads  2100  to  2100  Ibs.  sq.  ft. 

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Fig.  42. 


CONCRETE    CULVERTS   AND    TRESTLES.     201 

Slabs  with  beams  7  feet  apart  are  economical  for 
spans  from  14  to  20  feet  in  length. 

Slabs  with  beams  8  feet  apart  are  economical  for 
spans  from  20  to  30  feet  in  length. 

The  comparative  cost  chart,  Figure  42,  was  ob- 
tained from  130  separate  estimates,  and  the  conclu- 
sion from  it  is  that  slabs  for  the  above  loads  are  not 
economical  for  greater  lengths  than  8  feet  or  greater 
thicknesses  than  12  inches. 

Figures  43,  44  and  45  are  typical  drawings  for 
single  and  double  box  railroad  culverts  for  both 
slab,  and  a  combination  of  beam  and  slab  construc- 
tion, and  Tables  VII,  VIII,  IX  and  X  give  the  cor- 
responding sizes,  quantities  and  costs  for  culverts 
varying  in  area  from  4  to  480  square  feet.  These 
tables  give  separately  the  quantities  and  cost  for 
the  two  portals  and  for  the  culvert  barrel  per  foot 
of  length,  and  also  the  lengths  and  total  costs  of 
culverts  for  six  different  heights  of  embankment, 
varying  from  10  to  50  feet. 

The  single  and  double  slab  culvert  tables  contain 
34  different  sizes  each,  varying  from  2  feet  by  2 
feet  to  12  feet  by  12  feet  for  each  opening,  while  the 
combined  beam  and  slab  culverts  contain  30  corre- 
sponding sizes  each,  varying  from  8  to  20  feet  in 
width,  and  from  4  to  12  feet  in  height.  The  esti- 
mated costs  of  these  culverts  for  banks  20,  30,  40 
and  50  feet  in  height  are  shown  in  Figure  46.  These 
curves  represent  the  cost  of  the  economic  forms, 
which  generally  have  openings  of  a  greater  height 
than  width,  such  as  4  feet  wide  by  6  feet  high,  either 


202 


Is.; 

Illil 


204        CONCRETE   BRIDGES   AND   CULVERTS. 


TABLE  VII 

REINFORCED  CONCRETE,  SINGLE  BOX,  RAILROAD 
CULVERTS— SLAB  CONSTRUCTION 

TO  ACCOMPANY  FIGURE  43 


1 

-S 

^r 

~ 

4 

Top  and  Bottom 

Sides.         [Quantities,  per  liri.  ft. 

2  Portals. 

af 

09 

Square  Rods. 

c.c. 

(Concrete,  In. 

Square  Rods 

C.C. 

Concrete.C.Y. 

A 

1 

M 

Concrete.C.Y. 

A 

1 

cc 

I 

1 

2 

2 

4 

6  ^/2/f  —  6" 

6  V4"—  12" 

.19 

22 

2.43 

1  .  78  

14 

2 

" 

'J 

6 

" 

i//  .  jo 

.23 

26 

2.91 

3.40 

27 

3 

3;  2 

6 

83^—9 

" 

*4  —18 

.28 

35 

3.69 

3.55 

23 

4 

" 

g 

9 

" 

"        " 

7 

"        15 

.34 

43 

4.50 

4.00 

32 

5 

4 

12 

" 

"         " 

S 

12 

.42 

51 

5.39 

4.50 

200 

44 

6 

" 

t] 

15 

"        " 

9 

10 

.51 

62 

6.55 

6.00 

250 

58 

7 

4 

2 

8 

93^  —  71  / 

(5 

18 

.36 

58 

5.25 

3.85 

40 

8 

" 

3 

12 

"  "        " 

7 

15 

.42 

55 

5.60 

4.30 

34 

9 

" 

4 

16 

8 

12 

.50 

65 

6.66 

5.50 

250 

54 

10 

5 

20 

"         " 

9 

"       10 

.59 

75 

7.75 

6.80 

300 

66 

11 

" 

6 

24 

" 

"        " 

10 

8 

.69 

92 

9.26 

8.70 

500 

89 

12 

5 

3 

15 

103^-7 

8 

15 

.55 

66 

7.06   5.00 

500 

72 

13 

4 

20 

"        " 

9 

12 

.64 

75 

8.10  6.70 

600 

65 

14 

" 

5 

25 

" 

"        " 

10  "        10 

.74 

86 

9.42  8.50 

800 

84 

15 

" 

6 

30 

" 

tt             tt 

10 

8 

.79101 

10.3710.40 

1000107 

16 

" 

8 

40  "  i  " 

12 

6 

1.04132 

13.6013.00 

1600136 

17 

(5 

4 

24 

12:%  7 

10 

7^  —12 

.83113 

11.2210.00 

900116 

18 

36 

" 

it              tl 

10 

"        10 

.96134 

12.9712.40 

1200147 

19 

" 

8 

48 

" 

"        " 

12 

8 

1.20168 

16.3013.70 

1800173 

20 

" 

10 

60 

" 

"        " 

14 

6 

1.4? 

216 

20.6015.00 

2200208 

21 

8 

4 

3214 

12 

12 

1.18139 

15.0012.00 

900132 

22 

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(i 

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«         « 

12 

10 

1.33185 

18.0022.00 

1800248 

23 

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8 

64" 

"         " 

12 

8 

1.47215 

20.4030.00 

2200328 

24 

"10 

80  " 

tt             tt 

14 

6 

1.76265 

24.7043.00 

3200472 

25 

10  4 

4017 

1  51,4 

If) 

1  —15 

1.71241 

23.3018.00 

1400200 

26 

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6 

60 

« 

"       " 

15 

12 

1.84266 

25.4028.00 

2200312 

27 

" 

8 

80 

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15 

12 

2  .  07  282 

27.9037.00 

3200424 

28 

"ilOlOO 

"  "       " 

IS 

10 

2.50324 

32.9046.00 

4000'528 

29 

"12120 

" 

"       " 

IS 

8 

2.88381 

38.3057.00 

5000*656 

30 

12  4 

48 

20  1  —  4'4 

IS 

15 

2.33327 

31.8023.00 

1800256 

31 

"6 

72 

18 

12 

2.56362 

34.9037.00 

2800'378 

1)2 

"8 

96 

18 

12 

2.78378 

37.3052.00 

4000576 

33 

"10 

120 

" 

20 

10 

3.00412 

40.4068.00 

5000  744 

34  " 

12 

144 

" 

120 

8 

3.40466 

45.80J82.00 

6500916 

CONCRETE    CULVERTS   AND    TRESTLES.     205 


TABLE  VII— Continued 

REINFORCED  CONCRETE,  SINGLE  BOX,  RAILROAD 

CULVERTS— SLAB  CONSTRUCTION 

TO  ACCOMPANY  FIGURE  43 


10  ft.  Bank. 

15  ft.  Bank. 

20  ft.  Bank. 

30  ft.  Bank. 

40  ft.  Bank. 

50  ft.  Bank 

M 
~S> 

j 

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3 

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106 

54 

145 

69 

182 

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129 

327 

159 

400 

1 

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122 

51 

175 

66 

219 

96 

305 

126 

392 

156 

479 

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69 

283 

99 

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501 

159 

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727 

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538 

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116 

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312 

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417 

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524 

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737 

124 

947 

154 

1162 

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31 

315 

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427 

61 

547 

91 

772 

121 

1050 

151 

1295 

1,3 

28 

348 

43 

489 

58 

630 

88 

914 

118 

1194 

148 

1484 

14 

25 

365 

40 

532 

55 

675 

85 

987 

115 

1297 

145 

1607 

15 

34 

598 

49 

801 

79 

1206 

109 

1616 

139 

2016 

16 

31 

366 

46 

631 

61 

806 

91 

1136 

121 

1486 

151 

1816 

17 

25 

470 

40 

662 

55 

857 

85 

1247 

115 

1637 

145 

2017 

18 

34 

725 

49 

762 

79 

1453 

109 

1943 

139 

2433 

19 

. 

28 

783 

43 

1090 

73 

1708 

103 

2328 

133 

2928 

20 

30 

582 

45 

807 

60 

1032 

90 

1482 

120 

1932 

150 

2382 

21 

. 

40 

968 

55 

1238 

85 

1778 

115 

2318 

145 

2848 

22 

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34 

1020 

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1328 

79 

1938 

109 

2548 

139 

3148 

23 

28 

1157 

43 

1522 

73 

2262 

103 

3072 

133 

3732 

24 

30 

900 

45 

1250 

60 

1600 

90 

2300 

120 

3000 

150 

3700 

25 

39 

1297 

54 

1682 

84 

2442 

L14 

3192 

144 

3962 

26 

33 

1339 

48 

1754 

78 

2594 

108 

3424 

138 

4244 

27 

27 

1413 

42 

1908 

72 

2888 

102 

3878 

132 

4849 

28 

36 

2036 

66 

3176 

96 

4316 

[26 

5456 

90 

29 

1166 

44 

1656 

59 

2126 

89 

3076 

119 

4026 

149 

4978 

^  J 

30 

38 

1698 

53 

2218 

83 

3278 

.13 

49Q8 

4.Q 

KCMC 

01 



32 

1766 

47 

2326 

77 

3436 

107 

*±^fi7o 

4536 

LrrO 

137 

OO^o 

5676 

>i 
32 

26 

1794 

41 

2394 

71 

3604 

101 

4814 

131 

6024 

33 

35 

2516 

65 

3886 

95 

5266 

125 

6636 

34 

206        CONCRETE  BRIDGES  AND   CULVERTS. 

TABLE  VIII 

REINFORCED  CONCRETE,  DOUBLE  BOX,  RAILROAD 

CULVERTS— SLAB  CONSTRUCTION 

TO  ACCOMPANY  FIGURE  44 


1 

•t 

~ 

I 

e 

.j 

O  ^4 
'-£    ^ 

Top  and  Bottom] 

Sides.            Quantities  per  ft. 

2  Tortals. 

Concrete,  In. 

'quareRod: 

c.c. 

j 

•Square  Rod 

C.  C. 

Concrete.C.Y. 

A 

I 

1 

Concrete.C.Y. 

A 

i 

OS 

i 

1 

2 

2 

8 

6 

6 

4"—  6" 

6'W—  12" 

.32 

51 

4.60 

2.6;       0 

20 

2 

" 

3 

12 

" 

" 

«       « 

e 

10 

.38 

43 

4.72 

3.9 

0 

31 

3 

3 

3 

18 

9 

8  a^  —9 

7 

3/£  —15 

.61 

76 

7.94 

4.9 

0 

39 

4 

" 

4 

24 

" 

" 

"       " 

8 

12 

.72 

89 

9.30 

5.3 

200 

50 

5 

" 

5 

30 

" 

" 

"       " 

9 

10 

.8410410.85 

7.0 

250 

66 

6 

4 

3 

24 

12 

9  34  _7  14   7 

15 

.82101 

10.52 

5.5 

0 

44 

7 

" 

4 

32 

" 

" 

"       " 

8 

12 

.94114 

12.05 

6.6 

250  62 

8 

" 

5 

40 

" 

" 

"       " 

9 

"        10 

1.08129 

13.65 

8.0 

300|  76 

9 

" 

6 

48 

« 

u 

"       " 

10 

8 

1.19152 

15.60 

10.0 

500100 

10 

5 

3 

30 

12 

103^  —7 

8 

15 

1.08123 

13.50 

6.7 

600|  77 

11 

" 

4 

40 

" 

" 

"       " 

9 

12 

1.21 

135 

15.10 

8.2 

700  89 

12 

" 

5 

50 

" 

. 

"       " 

10 

10 

1.35 

151 

16.81 

9.7 

800101 

13 

" 

6 

60 

" 

" 

"       " 

11 

8 

.51 

174 

19.0212.6 

1000140 

14 

" 

8 

80 

« 

" 

"       « 

12 

6 

.79 

232 

23.6515.0 

1600184 

15 

6 

4 

48 

12 

12%  -7 

10%  -12 

.62 

206 

21.1011.0 

900124 

16 

" 

6 

72 

" 

" 

"       " 

11 

10 

.89239 

24.5018.0 

1200192 

17 

11 

8 

96 

" 

" 

"       " 

12 

8 

.20285 

29.0024.0 

1800264 

18 

"  10  120 

" 

" 

"       " 

14 

6 

.62353 

35.5030.0 

2400336 

19 

8 

41  64 

15 

14 

7^  5  1// 

12 

12 

.35 

306 

30.9014.0 

900148 

20 

" 

6  96 

" 

" 

"  •      "  ' 

12 

10 

.65 

338 

33.7020.0 

2000246 

21 

" 

8128 

" 

" 

"         " 

12 

8 

.95 

384 

38.9027.02700304 

22 

« 

10160 

« 

« 

(1       •« 

14 

6 

.36 

457 

45.3037.03200424 

2310 

4  80 

15 

17 

i  —  sms 

1  —15 

3.36 

462 

45.5015.0 

1400176 

24 

" 

6120 

" 

" 

15| 

12 

3.75 

498 

49.6025.0 

2200288 

25 

" 

8160 

"      " 

15 

12 

4.11 

522 

53.5037.0 

3200424 

26 
27 

28 

12 

10200 
12240 

4  96 

18 

20 

1   —4^ 

IS 
IS 
IS 

10 
8 
15 

4.70577 
5.10660 
4.62647 

60.5047.04000536 
66.8062.05000696 
62.8020.01800232 

29 

" 

6144 

" 

" 

"   -jis 

12 

5.08685 

67.6035.02800 

392 

30 
31 
32 

" 

8192 

1  O  OOO 

!_->*>> 

" 

«] 

'<        " 

IS 

2!) 
20 

12 
10 

8 

5.50708 
6.02759 
6.55'838 

71.7045.04000520 
78.0062.05000,696 
85.0075.06500'860 

CONCRETE    CULVERTS   AND    TRESTLES.      207 

TABLE  VIII— Continued 

REINFORCED  CONCRETE,  DOUBLE  BOX,  RAILROAD 
CULVERTS— SLAB  CONSTRUCTION 

TO  ACCOMPANY  FIGURE  44 


10  ft.B'k!5  ft.  Bank.!20  ft.  Bank  30  ft.  Bank 

40  ft.  Bank. 

50  ft.  Bank. 

.d 

J 

V* 

1 

1 
& 

&» 

JS 

t 

JS 

.d 

•a 

1 

<y& 

1 

I 

-a  «-   fc 
III 

1 
o 

39 

200  54  269 

66 

335 

99  475  139  610  159!   750  1 

36  201  51 

272 

66 

341 

96 

482 

126 

623  156 

763 

2 

35 

315  50 

434 

65 

551 

95  789 

125 

1029  155 

1269 

3 

32 

347  47 

486 

62 

625 

92 

905 

122 

1180!  152 

1470 

4 

29 

381  44 

542 

59 

706 

89 

1031 

119 

1356 

149 

1686 

5 

35 

414 

50 

569 

65 

729 

95 

1064 

125 

1384 

155 

1674 

6 

32 

447  47 

627 

62 

807 

92 

1172 

122 

1522 

152 

1882 

7 

29 

471  44 

676 

59 

881 

89 

1286 

119 

1696 

149 

2106 

8 

26 

505!  41 

740 

56 

970 

86 

-1440 

116 

1900 

146 

2370 

9 

34 

535  49 

729 

64 

939 

94 

1337 

124 

1747 

154 

2147 

10 

31 

555 

46 

780 

61 

1009 

91 

1459 

121 

1909 

151 

2359 

11 

28 

579 

44 

849 

58 

1079 

88 

1589 

118 

2089 

148 

2579 

12 

25 

622 

40 

906 

55 

1196 

85 

1766 

115 

2316 

145 

2906 

13 

34 

984 

49 

1344 

79 

2044 

109 

2754 

139 

3465 

14- 

31 

779 

46 

1094 

61 

1414 

91 

2044 

121 

2684 

151 

3324  15 

25 

802 

40 

1172 

55 

1532 

85 

2262 

115 

2992 

145 

3712 

16 

34 

1244 

49 

1684 

79 

2544 

109 

3414 

139 

4264 

17 

28 

1326 

43 

1856 

73 

2916 

103 

4086 

133 

5036 

18 

301073  45 

1528 

60 

1998 

90 

2918 

120 

3848 

150 

4768 

19 

....1  40 

1586 

55 

2096 

85 

3106 

115 

4116 

145 

5096 

20 

....34 

1624 

49 

2204 

79 

3364 

109 

4544 

139 

5654 

21 

.  28 

1684 

43 

2364 

73 

3724 

103 

5074 

133 

6424 

22 

301536  45 

2226 

60 

2896 

90 

4276 

120 

5596 

150 

6976 

23 

39 

2218 

54 

2968 

84 

4458 

114 

5938 

144 

7408 

24 

" 

. 

33 

2184 

48 

2984 

78 

4584 

108 

6174 

138 

7774 

25 

27 

2166 

42 

3066 

72 

4886 

102 

6786 

132 

8536 

26 

36 

3096 

66 

5096 

96 

7098 

126 

9096 

27 

292052 

44 

2982 

59 

3932 

89 

5812 

119 

7882 

149 

9532 

28 

38 

2Q50  53 

3960 

83 

5992 

113 

7990 

143 

10040 

29 

.. 

32  2800  47 

3920 

77 

6020 

107 

8170 

137 

10320 

30 

26'  2716 

41 

28P6 

71 

6216 

101 

85Q6 

131 

10896 

31 

35  3830 

65  6370 

96  8960  125 

11460 

32 

208        CONCRETE  BRIDGES  AND   CULVERTS. 


TABLE   IX 

REINFORCED  CONCRETE,  SINGLE  BOX,  RAILROAD 

CULVERTS— BEAM  AND  SLAB  CONSTRUCTION 

TO  ACCOMPANY  FIGURE  45 


Top  and  Bottom 

Sides. 

Per  Lineal  ft. 

2  Portals. 

« 

« 

-§ 

•o 

1 

£ 

1 

Square 

Square 

5 

A 

«'    A 

•£ 

I, 

cS 

Rods. 

Rods. 

§ 

«« 

S         —  - 

«» 

1 

1 

1 

"° 

~ 

i 

•** 

1 

1 

1 

I 

3 

02 

I 

1 

8 

4 

32123   4—  1" 

12 

123—  y^r 

.9817714.6 

9.4   1250   125 

2 

" 

6 

48 

" 

4 

"        " 

" 

174-     " 

1.1020616.9 

15.7  2060J  206 

3 

" 

8 

64 

" 

u           u 

" 

224-% 

1.2724019.7 

23.2  3050  305 

4 

" 

10 

80  " 

"        " 

"  1274—1 

1.4827822.9 

32.  0|  4220  432 

5 

10 

4 

401436 

4—  IK  14133—  % 

1.2622319.1 

13.5 

1800   180 

( 

" 

6 

60 

' 

u             if 

" 

164—  % 

1.37 

26021.3 

21.2 

2800  280 

7 

" 

8 

80 

1 

It                U 

" 

214-% 

1.56 

29624.3 

30.6 

4050 

405 

8 

" 

10100 

" 

* 

It                U 

" 

26 

4  —  1 

1.78 

336'27.6 

41.5 

5500 

550 

9 

" 

12 

120 

" 

< 

"      " 

"304-1K 

2.00 

38131.1 

53.5 

7100 

710 

K 

12 

4 

48 

16 

40 

4  —  1^ 

16143—  ^ 

1.57 

28123.8 

16.5 

2200 

220 

11 

" 

6 

72 

" 

' 

"      " 

" 

154—  % 

1.69 

31926.2 

25.8 

3400 

340 

12 

" 

8 

96 

" 

• 

" 

«< 

194—  % 

L.  88  35729.  2 

36.5 

4800 

485 

13 

" 

10 

120 

1 

"      " 

"244-1   ' 

2.10403|32.9 

52.5 

7000 

700 

14 

" 

12 

144 

i 

" 

"294—  IK 

2.3745237.1 

64.0 

8500 

850 

15 

14 

6 

8418 

50 

5-1% 

18194—  %2.  35,388  34.  3 

40.0 

5300 

530 

16 

" 

8 

112 

u 

u 

"214—1     2.55456138.5 

55.0 

7200 

730 

17 

" 

10 

140 

u 

'      « 

' 

264—11^2.84 

50442.8 

72.0 

9600 

960 

18 

" 

12 

168 

" 

u 

'       " 

"315—  IK  3.  08  559  46.  9 

91.0121001210 

19 

16 

6 

86 

2054 

6—1%  20204—  %[2.8249142.2 

49.  0|  65001  650 

20 

" 

8 

128 

" 

" 

<       « 

"204—1     2.9854044.4 

64.0  8500  850 

21 

"10160 

" 

" 

i 

"254—  IK  3.  25  589  48.  4 

84.0111001110 

22 

"12192 

" 

" 

'       " 

"  29  5—  IK  3  •  50647  53  .  7  106  .  0  14000  1400 

23 

18 

610822 

58 

7-1% 

22204—  ^|3.32|572^ 

L9.4  60.0  80001  800 

24 

" 

8144 

" 

" 

"204 

I—  1     3.4762452.8  66.0  8800  880 

25 

]]  10'180 

M 

" 

" 

"244—  IK  3  .74  67756.01  99.0'l31001310 

26 
27 

28 

20 

12 
6 
81 

216 
L20 
L60 

24 

52 

*-W 

"285—  IK  4.  02  745  61.  8  122.  016200  1620 
2420^4—  %  3.  88  662  58.  7  71.0  94001  940 
"  20  4—1     4  .  05  724  61  .  2  93  .  0  12300  1230 

29 
30 

- 

10200 
12  240 

" 

« 

•• 

"i234—  1K4  •  30  776  65  .4117.  0  15500  1550 
"  27  5—  IK  4  .  60842j70  .  2  144  .  0;i9160jl910 

CONCRETE    CULVERTS   AND    TRESTLES.      209 


TABLE  IX— Continued 

REINFORCED  CONCRETE,  SINGLE  BOX,  RAILROAD 

CULVERTS— BEAM  AND  SLAB  CONSTRUCTION 

TO  ACCOMPANY  FIGURE  45 


10  ft.  Bank 

15  ft.  Bank 

20  ft.  Bank 

30  ft.  Bank 

40  ft.  Bank 

50  ft.  Bank. 

JS 

"Sb 
J 

» 

J3 

s 

I 

1 

«» 

I 

jA 

"8 
a 

•» 

J 

J 

•» 

! 

•» 

27 

535 

42\  735 

57 

973 

87 

1403 

117 

1843 

147 

2283 

1 

36|  816 

51 

1066 

81 

1566 

111 

2076 

141 

2576 

2 

30 

895 

45 

1190 

75 

1775 

105 

2365 

135 

2955 

3 

39 

1317 

69 

2002 

99 

2692 

129 

3372 

4 

25 

656 

40 

940 

55 

1230 

85 

1800 

115 

2360 

145 

2940 

5 

34 

1005 

49 

1320 

79 

1960 

109 

2600 

139 

3230 

6 

28 

1085 

43 

1455 

73 

2175 

103 

2905 

133 

3625 

7 

37 

1570 

67 

2400 

97 

3220 

127 

4050 

8 

31 

1675 

61 

2610 

91 

3530 

121 

4510 

9 

25 

820 

40 

1170 

55 

1530 

85 

2240 

115 

2950 

145 

367010 

34 

1230 

49 

1620 

79 

2500 

109 

3190 

139 

3980 

11 

28 

1300 

43 

1735 

73 

2605 

103 

3485 

133 

4355 

12 

.. 

37 

1910 

67 

2900 

97 

3870 

127 

4850 

13 

. 

31 

2000 

61 

3110 

91 

4210 

121 

5350 

14 

31 

1590 

46 

2110 

76 

3130 

106 

4150 

136 

5180 

15 

. 

25 

1690 

40 

2270 

70 

3430 

100 

4580 

130 

5730 

16 

34 

2420 

64 

3710 

,94 

5000 

124 

6260 

17 

28 

2520 

58 

3920 

88 

5310 

118 

6710 

18 

.  . 

30 

1920 

45 

2550 

75 

3810 

105 

5070 

135 

6350 

19 

. 

39 

2570 

69 

3900 

99 

5250 

129 

6550 

20 

.  . 

33 

2700 

63 

4080 

93 

5610 

123 

7030 

21 

27 

2850 

57 

4450 

87 

6050 

117 

7650 

22 

28 

2180 

43 

2920 

73 

4400 

103 

5850 

133 

7350 

23 

37 

2830 

67 

4410 

97 

5980 

127 

7530 

24 

31 

3050 

61 

4720 

91 

6410 

121 

8060 

25 

25 

3160 

55 

5020 

85 

6870 

115 

8720 

26 

28 

2580 

43 

3460 

73 

5200 

103 

6950 

133 

8740 

27 

37 

3500 

67 

5330 

97 

7180 

127 

8980 

28 

31 

3570 

61 

/>53fi 

91 

7450 

121 

9450 

?Q 

25 

3660 

55  5760 

85 

7860 

115 

991030 

210        CONCRETE  BRIDGES  AND   CULVERTS. 


TABLE    X 

REINFORCED  CONCRETE,  DOUBLE  BOX,  RAILROAD 
CULVERTS— BEAM  AND  SLAB  CONSTRUCTION 

TO  ACCOMPANY  FIGURE  45 


c 

Top  and  Bottom. 

Sides. 

Per  Lin.  ft. 

1 

! 

I 

J 

Rods. 

Rods. 

1 

& 

•5 

i 

<a     'S'-S 

t 

"of 

^r 

•a 

•§ 

&       j  *3  E~* 

J        '       W              6 

f* 

ffi 

•<      PH 

.a 

^ 

JO 

J3 

1 

8 

4     64   15 

12  294—1" 

12 

12!3—  M" 

1.80,     320  26.8 

2 

« 

6     96     " 

" 

' 

"         " 

" 

174-       " 

2.05     348 

30.3 

3 

(i 

8   128 

" 

"      " 

"         " 

" 

224-% 

2.32     388 

33.6 

4 

10   160 

" 

"      " 

"         " 

" 

27 

4—1 

2.61     433 

37.9 

5 

10 

4     80 

1.5 

14  334—  IK 

14 

133—  M 

2.08 

405 

33.0 

6 

6   120 

"      " 

"         " 

" 

164—  % 

2.33 

446 

36.3 

7 

" 

8   160 

" 

"      " 

"         " 

" 

214-  % 

2.62 

489 

40.1 

8 

10  200 

« 

" 

" 

"         " 

" 

26 

4—1 

2.91 

537 

44.4 

g 

" 

12  240 

" 

"      i< 

"         " 

" 

30 

4-1% 

3.42 

587 

50.8 

10 

12 

4     96 

18 

16!  37,4—  \\i 

16 

14 

3  ^ 

3.00 

510 

44.4 

11 

6   144 

«       « 

"         " 

" 

15 

4—  % 

3.25 

555 

48.0 

12 

« 

8   192 

" 

1 

«         « 

" 

19 

4-  % 

3.52 

601 

52.2 

13 

« 

10  240 

« 

" 

" 

24 

4—1 

3.86 

656 

57.2 

14 

" 

12|  288 

" 

"         " 

" 

294-1% 

4.21     710 

62.0 

15 

14 

6   168 

18 

18 

475—1% 

18 

194-  % 

4.38 

767 

65.5 

16 

8  224 

« 

"         " 

" 

214—1 

4.71 

825 

70.6 

17 

« 

10'  280 

" 

" 

" 

234—1% 

5.00     881 

75.0 

18 

" 

12  336 

" 

" 

" 

"         " 

" 

315—1% 

5.38     946 

80.7 

19 

16 

6 

192 

20 

20  506—1% 

20 

204-  % 

5.28     911 

78.2 

20 

8 

256 

" 

«      « 

'         " 

" 

204—1 

5.51     963 

82.1 

21 

« 

10 

320 

" 

"      " 

' 

" 

254-1% 

5.90   1024 

88.0 

22 

" 

12 

384 

" 

" 

" 

'         " 

" 

295-1% 

6.30 

1088 

94.0 

23 

18 

6 

216 

22 

22 

547—1% 

22 

20|4—  % 

6.25 

1069 

93.0 

24 

8 

288 

(i 

1         " 

" 

204—1 

6.55 

1130 

97.0 

25 

« 

10 

360 

" 

i        « 

" 

244—1% 

6.95 

1195102.5 

26 

» 

12 

432 

" 

"i 

<         « 

" 

285—1% 

7.38 

1263109.2 

27 

20 

6 

240 

24 

24 

588-1% 

24 

204-% 

7.40 

1251109.0 

28 

8 

320 

" 

" 

i         i< 

" 

204—1 

7.70 

1322114.0 

29 

" 

10 

400 

" 

" 

' 

" 

234-1% 

8.10 

1395119.5 

30 

12)  480     " 

" 

'         " 

" 

27|5—  1% 

8.50  1467 

126.5 

CONCRETE    CULVERTS   AND    TRESTLES.      211 


TABLE  X— Continued 

REINFORCED  CONCRETE,  DOUBLE  BOX,  RAILROAD 
CULVERTS— BEAM   AND  SLAB  CONSTRUCTION 

TO  ACCOMPANY  FIGURE  45 


2  Portals. 

10  ft.Bank 

15ft.  Bank 

20  ft.  Bank  30  ft.  Bank 

40  ft.  Bank. 

50  ft.  Bank.| 

Concrete,  Yds 

gg 

1 

O2 

«© 

1 

1 

3 

M 

1 

1 

»& 

I 

3 

M 
I 

J3 

1 
1 

i  &^ 
I 

jf 

"& 

J 

&» 

1 

.- 
U 

J 

M 

14.3 
22.6 
32.4 
43.0 
20.4 
31.5 
43.2 
53.5 
72.0 
26.0 
38.6 
53.5 
73.0 
87.0 
54.0 
71.0 
91.0 
111.0 
72.  Ol 
92  0 
117.0 
143.0 
91  0 
105.0 
145.0 
175.01 
98.0 
142.0 
176.01 
211.0; 

1910 
3000 
4300 
5700 
2720 
4200 
5720 
7100 
9500 
3450 
5100 
7100 
9700 
1160 
7200 
9400 
L2100 
L4700 
9600 
12200 
15500 
L9000 
12100 
L3SOO 
19200 
23200 
13000 
L8800 
23400 
28100 

191 
300 
430 
570 
272 
420 
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710 
950 
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116 
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CONCRETE    CULVERTS   AND    TRESTLES.      213 


Cost  of  Reinforced  Concrete  R.  R.  Culverts. 

Single  Track  Banks. 
Form—  Rectangular  Box. 

Base  Prices. 

Concrete  in  place  $8.00  per  yd. 
Steel  in  place  4c  per  Ib. 


V 


-4 


T~OT fit.    flft£fl  of 


100  2  So 


Fig.  46. 


214        CONCRETE   BRIDGES   AND   CULVERTS 

double  or  single.  Culverts  of  these  forms  cost  less 
for  any  given  area  than  if  made  with  wider  and 
shallower  openings.  The  reason  for  this  is  due  to 
the  fact  that  for  wider  openings  the  thickness  of 
cover  slabs  increase  more  rapidly  than  the  thickness 
of  side  walls. 

From  the  comparative  cost  chart,  Figure  46,  the 
following  conclusions  are  deduced: 

Single  box  slab  culverts  are  economical  for  areas 
up  to  50  square  feet. 

Double  box  slab  culverts  are  economical  for  areas 
up  to  75 -square  feet. 

Single  box  beam  and  slab  culverts  are  economical 
for  areas  up  to  125  square  feet. 

Double  box  beam  and  slab  culverts  are  economical 
for  areas  above  125  square  feet. 

Wide,  flat  culverts  cost  somewhat  more  than  nar- 
row and  higher  ones  of  the  same  area,  but  they  are 
more  effective  and  offer  less  resistance  to  the  free 
flow  of  water.  For  a  bank  of  any  given  height,  the 
low  culvert  will  have  a  longer  barrel  than  a  higher 
one,  though  this  will  be  offset  to  some  extent  by  the 
shorter  length  of  wing  walls.  There  is  little  or  no 
economy  in  reducing  the  length  of  culvert  barrel  by 
using  high  end  parapet  retaining  walls,  as  material 
thus  used  might  better  be  employed  in  increasing 
the  length  of  culvert  barrel,  thereby  causing  shorter 
wing  walls. 

Tn  proportioning  the  thickness  of  wing  walls, 
when  these  wings  are  placed  at  a  considerable  angle 
to  the  culvert  face,  the  stability  of  the  wing  wall  is 


CONCRETE    CULVERTS   AND    TRESTLES.      215 

thereby  greatly  increased,  and  it  is  generally  safe  to 
make  the  base  thickness  of  the  wings  near  their 
connection  to  the  abutment  from  20%  to  25%  of 
the  wing  wall  height.  Towards  the  ends  where 
the  wings  receive  no  support  from  the  culvert 
sides,  the  width  or  thickness  of  wing  wrall  base 
should  then  be  40%  of  the  unsupported  height. 

The  size  of  beams  and  slabs  given  in  Tables  VII, 
VIII,  IX  and  X  are  for  culvert  barrels  subjected  to 
the  loads  specified,  which  occurs  at  and  near  the 
center  of  the  embankment.  For  long  culverts,  these 
sizes  may  be  reduced  towards  the  ends  where  the 
loads  are  somewhat  less  than  at  the  middle. 

Where  the  nature  of  the  soil  will  permit,  some 
economy  may  result  by  omitting  the  reinforced  con- 
crete pavement  slab,  and  substituting  offset  foot- 
ings under  the  side  walls,  as  shown  on  the  concrete 
trestle  plans,  Figures  58  to  65  inclusive,  using  a 
cobble  stone  pavement,  if  required. 

There  is  less  probability  of  debris  and  drift  col- 
lecting when  the  culvert  bottom  is  curved  or  dished 
out  at  the  center,  than  wThen  built  flat  or  horizontal 
between  the  two  side  walls.  Box  culvert  corners 
should  be  braced  with  straight  or  curved  corner 
fillets,  reinforced  with  diagonal  rods,  as  shown  on 
the  typical  drawings. 

It  is  unnecessary  to  increase  the  thickness  of  side 
walls  from  the  top  to  the  bottom,  excepting  perhaps 
for  high  culverts,  and  even  then  since  the  condition 
of  earth  pressure  on  the  side  walls  is  uncertain,  any 
effort  at  ultra-refinement  is  unnecessary. 


216        CONCRETE   BRIDGES  AND   CULVERTS. 

"Waterproofing  should  be  used  on  the  exterior 
surfaces  of  the  roof  and  sides  to  prevent  drainage 
water  from  soaking  into  the  concrete.  The  ad- 
hesion of  concrete  to  steel  is  decreased  about  100% 
when  the  concrete  is  continuously  water  soaked, 
and  this  decrease  can  be  avoided  by  finishing  the 
outer  surface  of  the  top  and  sides  with  a  coating  of 
neat  cement  or  other  waterproof  material. 

Comparative  Costs  of  Culverts  of  Various  Forms, 
Figure  47  shows  the  comparative  costs  of  reinforced 
concrete  box  railroad  culverts  compared  with  corre- 
sponding costs  of  culverts  of  other  forms.  The 
chart  gives  the  total  cost  of  culverts  for  an  embank- 
ment 20  feet  in  height,  and  for  cross-sectional  areas 
varying  from  5  to  200  square  feet. 

The  new  reinforced  concrete  box  culverts,  the  cost 
of  which  are  shown  by  the  heavy  line  number  10, 
are  more  economical  than  any  other  permanent  cul- 
verts, and  cost  but  little  more  than  wooden  box 
culverts.  They  range  in  cost  from  30  to  50  cents 
per  square  foot  of  sectional  area. 

The  various  culverts,  the  costs  of  which  are  shown 
in  Figure  47  by  lines,  are  as  follows : — 

No.  1  gives  the  cost  of  standard  cast  iron  pipe 
culverts,  which  are  suitable  only  for  small  openings, 
and  while  they  can  be  quickly  placed,  and  some- 
times inserted  inside  of  worn-out  temporary  wooden 
box  culverts,  they  are  not  economical. 

No.  2  are  reinforced  concrete  box  culverts  with 
bottoms,  similar  to  those  in  use  on  the  Union  Pacific 
and  Southern  Pacific  railroads, 


CONCRETE    CULVERTS    AND    TRESTLES.      217 
Comparative  Costs  of  Culverts. 

SINGLE   TRACK   RAILROAD.      HEIGHT   OF   BANK   2Q   FEET. 

No.  1  Cast  iron  pipe. 

"  2  Reinforced  concrete  box,  with  bottoms. 

"  3  Rail  top  concrete  box. 

"  4  Reinforced  concrete  arch. 

"  5  Solid  concrete  arch. 

"  6  Stone  arch,  Baker's  standard. 

"  7  Reinforced  concrete  box,  no  bottoms. 

u  8  Rubble  stone  box. 

"  9  Wood  box. 

"  10  Reinforced  concrete  box,  new  standard. 


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20^ 

218        CONCRETE   BRIDGES   AND    CULVERTS. 

No.  3  are  concrete  rail  top  culverts  having  slabs 
15  to  18  inches  thick,  and  reinforced  with  rails 
spaced  38  inches  apart  for  a  6-foot  span,  10  inches 
apart  for  an  8-foot  span,  and  6  inches  apart  for  a 
10-foot  span. 

Xo.  4  are  reinforced  concrete  arches,  similar  to 
those  in  use  on  the  above  named  railroads. 

Xo.  5  are  concrete  arches  without  reinforcement. 

Xo.  6  are  segmental  stone  arch  culverts  as  pro- 
posed by  Mr.  Baker  in  his  book  on  Masonry  Con- 
struction. 

Xo.  7  are  reinforced  concrete  box  culverts,  similar 
to  Xo.  2,  excepting  that  they  are  without  bottoms 


2:— Portals 

Concrete  72  yds.  ®  $8.00  ==  $576 
Steel     3450  Ibs.  @     .04=   13S 

*714 
Barrel  per  lln.  ft. 

Concrete 468yds.  (&  $8.00=$374 

Steel         450  Ibs.  @     .04=  180 

$554 

Length  for  20  ft.  bank  =  32. 
Area  =  180  sq.  ft.     Cost  $2490. 


Fig.  48. 


CONCRETE    CULVERTS   AND    TRESTLES.      219 

and    cost    proportionately    less.     They    have    offset 
footings  under  the  side  walls. 

No.  8  are  rubble  stone  box  culverts,  the  kind  most 
commonly  used  by  the  railroads  until  recently,  for 
small  openings. 

No.  9  are  wooden  box  culverts,  and  while  they  are 
not  permanent,  they  have  the  merit  of  being  the 
least  expensive  of  all. 

No.  10  are  the  new  standard  reinforced  concrete 
box  culverts,  as  shown  in  Figures  43,  44  and  45, 
the  quantities  and  cost  of  which  are  given  in  Tables 
VII,  VIII,  IX  and  X. 

An  actual  cost  record  for  building  a  4-foot  con- 
crete arch  culvert  under  a  railroad  embankment  in 
Idaho,  during  the  thirty  days  from  June  5th  to  July 
llth,  1903,  is  as  follows  :— 

Foundations  contain  111  yards,  and  cost $5.00  per  yd. 

Upper  part  contains  137  yards,  and  cost 7.00  per  yd. 

Average  cost  about   6.00  per  yd. 

Cost  of  whole  culvert  per  cu.  yard  of  concrete.  10. 00  per  yd. 

Portland  Cement  used,  272  barrels.   Cost 2.70  perbbl. 

Foreman  paid $150.00    per   month. 

1  Finisher  paid 3.00  per  day 

Laborers    paid 2.00  per  day 

4  Carpenters  paid 3.00  per  day 

Labor  cost   $1723.00 

Material    cost  830.00 


Total    $2553.00 

Concrete   made   entirely   from   sand   and   gravel   at   rail- 
road company's  pit,  without  any  broken  stone. 

Other  Common  Culvert  Forms.    Figures  48  to  57 
inclusive,  show  other  forms  of  culverts,  and  Table 


220        CONCRETE   BRIDGES  AND   CULVERTS 

XI  contains  their  estimated  quantities  and  costs. 
For  the  purpose  of  comparing  these  with  others,  the 
costs  have  been  estimated  for  lengths  required 
under  a  20-foot  embankment,  and  these  costs  are 
given  in  Figure  47,  together  with  their  correspond- 
ing numbers.  They  vary  in  cost  from  26  to  36  cents 
per  square  foot  of  section  area,  for  each  lineal  foot 
of  culvert. 

Figure  48  is  a  reinforced  concrete  box  culvert  12 
feet  high  and  15  feet  wide,  with  rod  reinforcement, 
similar  to  the  new  single  box  slab  culvert.  For  so 
large  a  section  area,  the  slab  type  is  not  economical. 

Figure  49  is  a  reinforced  concrete  box  culvert  of 
combined  beam  and  slab  construction,  12  feet  high 


2  Portals:— 
Concrete  74  yds.@s8.00 
Steel      4720  Ibs.  @    .04 


Barrel  per  ft. 
Concrete5 .  8yds.fr  *H.oo 
Steel        5151bs.@    .04 


Length  for  20  ft.  bank 
Area  =  230  square 
Cost  =  $2930. 


=  $592 

=  188 
$780 

=$464 
=  20.6 
$67.0 
=  32  ft. 
feet. 


Fig.  4i>. 


CONCRETE    CULVERTS   AND    TRESTLES.      221 


and  20  feet  wide.  For  an  area  of  this  size  a  more 
economical  form  is  secured  by  using  a  double  box 
of  the  same  general  type. 

Figure  50  is  a  beam  top  culvert,  12  feet  high  and 
15  feet  wide.  The  culvert  top  is  arched  3  feet  and 
the  arch  strength  is  considered  when  proportioning 


2  Portals:— 
Concrete  88yds.  @  $8.00=4704 

Barrel  per  lln  ft. 
Concrete  6.  lyds.  @$8.00=$48.8 
Steel        240  Ibs.  @    .04=    9.6 
$58Ti 

Length  for  20  ft.  Bank=32  feet. 

A  rea  =  161  sq.  ft.     Cost = $2570. 


Fig,  50. 

the  thickness  of  the  culvert  top.  Culverts  similar  to 
this  have  been  used  by  the  Illinois  Central  Railway 
Company. 

Figure  51  is  a  concrete  box  culvert  with  rod  rein- 
forcement similar  to  Figure  58,  excepting  that  in 
it  offset  footings  and  cobble  stone  pavement  are 
used  instead  of  a  reinforced  concrete  pavement  slab. 


222        CONCRETE   BRIDGES   AND   CULVERTS. 


< 1 


2  Portals:— 

Concrete  88  yds.  @$8.00=$704 
Barrel  per  lin.  ft. 

Concrete  6. 2  yds.  @$8.00=$49.0 

Steel  150  Ibs.  @  .04=  66 
$556 

If  foundation  is  depressed  as 
shown  dotted,  then  area  =  172 
square  feet. 

Length  for  20  ft.  bank=32ft. 
Cost =$2480. 


Fig.  51. 


Figure  52  is  a  reinforced  concrete  box  culvert  of 
beam  and  slab  construction,  12  feet  high  and  20  feet 
wide.  For  so  large  an  area,  a  double  box  of  the 
same  type  will  be  more  economical. 

Figure  53  is  a  culvert  of  the  same  dimensions  as 
Figure  52,  with  solid  concrete  side  walls,  bottom 
cobblestone  pavement,  and  roof  reinforced  with  dou- 
ble lines  of  60-pound  track  rails,  united  with  %-inch. 

Figure  54  is  a  reinforced  concrete  arch  culvert 
with  buttressed  side  wralls  and  slab  pavement. 
Structures  similar  to  this  are  used  by  the  Northern 
Pacific  Railroad. 


CONCRETE    CULVERTS    AND    TRESTLES.      223 


'^^^^7^''' 


QUANTITIES 
2  Portals:— 

Concrete  113 yds.  fi  $8.00=1904 
Steel      14500  Ibs.  (a,     .04=  580 
11484 
Barrel  per  lin.  ft. 

Concrete4.fi  yds.  (ft  $8.00=$36.8 
Steel         700  Ibs.  @     .04=  280 
$64.8 

Length  for  20  ft.  bank =25  ft. 
Ar ea  =  240  sq.  f t .     Cost  $3 1 00. 


Fig.  52. 

Figure  55  is  a  beam  top  culvert  12  feet  high  and 
20  feet  wide,  similar  to  Figure  50.  It  will  be  seen 
that  neither  of  these  types  are  economical. 

Figure  56  is  a  parabolic  arch  culvert. 

Figure  57  is  a  reinforced  concrete  arch  culvert 
possessing  greater  merit  than  any  other  form  of 
arch  culvert  now  in  use.  It  contains  the  least 
amount  of  material,  the  saving  being  chiefly  in  the 
sides.  Masonry  arch  culverts  of  the  old  type, 
whether  built  of  stone  or  concrete,  have  the  greater 
part  of  their  material  in  the  side  walls  or  abutments. 
Figure  57  is  designed  similar  to  a  tunnel  center,  or 
a  sewer  arch,  and  its  form  and  light  construction 


224        CONCRETE  BRIDGES  AND  -CULVERTS. 


are  possible  only  because  of  the  presence  of  rein- 
forcing metal  in  the  arch  ring.  Culverts  of  this 
general  form  are  being  used  by  several  of  the  rail- 
road companies  and  are  economical.  They  have  a 
disadvantage,  however,  in  requiring  the  use  of 
curved  forms,  but  this  is  overcome  to  some  extent 
by  using  collapsible  centers. 

A  modification  of  this  form  of  culvert  using  a 
semicircular  top,  is  also  shown  in  Figure  57. 

Mr.  Luten's  rules  for  proportioning  such  arches 
under  railroad  banks,  in  spans  of  50  feet  or  less, 
and  with  a  depth  of  earth  filling  above  of  not  less 
than  10  feet,  are  as  follows  :  — 

Crown  Thickness  D.= 


30 


2  Portals:— 

Concrete  88  yds.  @  $8.00  $701 
Barrel  per  lin.  ft. 

Concrete  8  yds.  @  $8.00  =  $64.00 

Steel  1015  Ibs.  @  .015=  15.22 
$7V».22 

Length  for  20  ft.  bank  =  30  ft. 

Area  =  250  sq.  ft.     Cost  $30hO. 


Fig.  53. 


CONCRETE    CULVERTS    AND    TRESTLES.      225 
span 

:^o" 

Back  of  abutments  batter  one  in  four. 
The    number    of   square    inches    of    steel   for    one 
edge  per  lineal  foot  of  arch  is 


__ 

400,000  D. 

L  is  the  live  load  in  pounds  that  can  be  concen- 
trated on  the  half  arch  for  one  track. 


2  Portals: — 

Concrete  47yds.  @  $8.00  =  $376 
Steel       1600  Ibs.  @      .04=     64 
$140 

Barrel  per  ft. 

Concrete  3. lyds.  @  $8.00=$24.8 
Steel         170  Ibs.  @     .04=     6.8 
$31.6 

Area  =  92  sq.  ft,  Length  for  20  ft. 
bank  =  42  ft.  Cost  for  20  ft. 
bank,  $1780. 


±  re, 


Fig.  54. 


226        CONCRETE   BRIDGES    AND    CULVERTS. 


C704 


2  Portals:— 

Concrete  88  yds.  (&,  $8.00 
Barrel  per  ft. 

Concrete  7.25  yds.  <u  $8.00=$58.0 
Steel         460  Ibs.  fa,      .04=  18.4 
$76  4 

Length  for  20  ft.  bank  =  32  ft. 
Area  =  215  sq.  It.     Cost  $3150. 


Fig.  55. 


'2   1  Portals:— 

Concrete  43.4yds.  (at8.00=?347.2 
Steel        2670  Ibs.  @     .04=  106.8 
$454.0 

Barrel  per  ft. 

Concrete  3.3  yds.  @  $8.00  =  $26.4 
Steel         230  Ibs.  @     .04=     9.2 
$35.6 

Area  =  128  sq.  ft.  Length  for 
20  ft.  bank  =  39  ft.  Cost  for  20  ft. 
bank,  $1844. 


Fig.  56, 


CONCRETE    CULVERTS    AND    TRESTLES.      227 

R  is  the  height  in  feet,  and  D  the  crown  thickness 
in  inches. 


Fig.  57. 

TABLE  XI 

CULVERT  DATA,  FIGURES  48  TO  56 


.1  1  ?  I 

Barrel,  per  ft. 

2  Portals 

|20ft 

Bank, 

tj  0  » 

e'.5"E 

O  3  03 

1 

03 

I 

III 

1 

i 

1 

-a" 

! 

CQ  "c 

II 

48  15 
49  20 
50  15 
51   15 
52  20 
53  20 
54  10 
55  20 
56  16 

12 
11 
11 
11 
12 
12 
10 
11 
10 

180 
230 
161 
172 
240 
250 
92 
215 
128 

4.7 
5.8 
6.1 
6.2 
4.6 
8.0 
3.1 
7.2 
3.3 

450 
515 
240 
150 
700 
1015 
170 
460 
230 

55.4 
67.0 
58.4 
55.6 
64.8 
79.1 
31.6 
76.4 
35.6 

72 
74 
88 
88 
113 
88 
47 
88 
43 

3450 
4720 

14500 

'ieoo 

'2670 

714 
780 
704 
704 
1484 
704 
440 
704 
454 

32 
32 
32 
32 
25 
30 
42 
32 
39 

2486 
2924 
2572 
2483 
3104 
3077 
1784 
3148 
1844 

30.8 
29.1 
36.4 
32.4 
27.0 
31.8 
34.4 
35.5 
27.8 

228        CONCRETE  BRIDGES  AND   CULVERTS. 

CONCRETE   RAILROAD   TRESTLES. 

Figures  58,  59  and  61  to  65  inclusive  show  five 
different  types  of  reinforced  concrete  railroad  tres- 
tles. In  connection  with  these  and  for  the  purpose 
of  comparison,  a  diagram  and  table  of  dimensions  is 
given  in  Figure  60,  for  double  track  steel  beam 
bridges,  a  type  generally  in  use  by  the  railroad  com- 
panies for  short  spans.  The  drawings  for  these  dif- 
ferent types  of  concrete  trestles  show  double-track 
structures,  28  feet  wide  with  15  inches  of  filling, 
sufficient  only  for  the  usual  depth  of  ballast.  When 
headroom  or  other  conditions  will  permit,  additional 
space  for  earth  filling  beneath  the  ballast  should  be 
provided,  making  a  minimum  depth  from  base  of 
rail  to  concrete  of  not  less  than  3  feet.  In  many 
bridges  this  depth  has  been  exceeded.  The  arch 
viaduct  over  the  Santa  Ana  River  at  Riverside,  Cali- 
fornia, has  a  depth  of  5  feet  from  the  base  of  rail  to 
the  extrados  at  the  crown. 

These  trestle  designs  marked  A  to  II  inclusive  are 
of  the  following  types : 
Double  Track  Structures. 

A.  Railtops.     Loads  carried  entirely  by  rails  in 
bending. 

B.  Beamtops.     Loads  carried  entirely  by  beams 
in  bending. 

C.  Standard  steel  beam  bridges.     Open  decks 

D.  Beamtops.     Beams  for  reinforcing  only. 

E.  Reinforced  concrete.     Slab  type.     Rod  rein- 
forcement. 


CONCRETE    CULVERTS    AND    TRESTLES:     229 

F.  Reinforced    concrete.     Beam   and   slab   type. 
Rod  reinforcement. 

SINGLE  TRACK  STRUCTURES. 

G.  Reinforced  concrete.     Slab  type.     Rod  rein 
forcement. 

II.  Reinforced  concrete.  Beam  and  slab  type. 
Rod  reinforcement. 

These  standard  trestles  were  designed  by  the  au- 
thor, without  special  reference  to  the  standard  cul- 
verts, and  also  under  a  somewhat  different  specifica- 
tion. Instead  of  making  an  impact  allowance 
amounting  to  50%  of  the  live  load  and  using 
a  700-pound  concrete  working  unit,  as  in  designing 
the  concrete  culverts,  the  standard  trestles  are  de- 
signed with  no  impact  addition  and  with  a  working 
unit  of  500  pounds  per  square  inch  for  concrete  in 
compression.  The  assumed  engine  load  is  Cooper's 
E  50,  which  is  equivalent  when  distributed  by  the 
ties,  rails  and  ballast  to  a  uniform  live  load  of  1,100 
pounds  per  square  foot.  To  this  is  added  the  weight 
of  track,  filling  and  concrete,  making  the  total  loads 
from  1,500  to  1,700  pounds  per  square  foot,  as  par- 
ticularly noted  on  the  various  figures.  The  founda- 
tions are  of  sufficient  width  so  the  bearing  pressure 
on  the  soil  will  not  exceed  three  tons  per  square 
foot.  For  the  purpose,  however,  of  making  the  esti- 
mates liberal,  the  pier  quantities  in  all  cases  include 
piles.  It  will  be  seen  that  on  each  plate  is  a  table 
giving  the  length  of  span,  thickness  of  concrete, 
size  of  metal,  and  the  quantities  of  concrete,  steel 
and  ballast,  together  with  the  estimated  costs  for 


230        CONCRETE  BRIDGES  AND   CULVERTS. 

the  various  spans.  In  connection  with  designs  B, 
D,  E  and  G,  there  are  also  tables  giving  the  sizes, 
quantities  and  costs  for  piers  of  various  heights. 
The  piers  vary  from  2  to  3  feet  in  thickness  at  the 
top,  depending  on  their  height,  and  they  have  side 
batters  of  1  in  24.  When  piers  have  a  less  height 
than  15  feet,  there  is  only  a  single  footing  course  at 
the  base,  but  for  heights  greater  than  15  feet  there 
are  2  footing  courses.  This  is  necessary  to  prevent 
the  load  on  the  soil  exceeding  3  tons  per  square 
foot- 
Economic  Span  Lengths.  The  designs  are  made 
for  spans  up  to  24  feet  in  length  and  piers  up  to 
30  feet  in  height,  and  are  suitable  for  structures 
within  these  limits.  The  economic  span  length  to 
use  for  any  given  height  of  trestle,  is  that  one  where 
the  cost  of  the  span  is  approximately  equal  to  the 
cost  of  pier.  The  cost  of  pier  for  the  given  trestle 
height  may  be  taken  directly  from  the  pier  tables, 
and  from  the  corresponding  table  giving  the  cost  of 
span,  a  length  may  be  selected,  the  cost  of  which  is 
approximately  equal  to  the  cost  of  the  pier.  Hav- 
ing thus  determined  the  economic  span  length,  the 
various  sizes  may  be  taken  directly  from  the  tables. 

Description  of  Various  Trestle  Designs. 

The  following  are  brief  descriptions  of  the  various 
trestle  designs  referred  to  above: — 

Design  A.  Figure  58.  This  is  a  type  that  has 
been  extensively  used  for  small  spans  up  to  12  feet 


30      t-      t-      •* 


50 

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232        CONCRETE  BRIDGES  AND   CULVERTS. 

in  length,  though  usually  restricted  to  a  length  of 
8  feet.  The  loads  are  carried  entirely  by  the  bend- 
ing resistance  of  the  rails.  Railroad  companies 
usually  have  a  large  stock  of  old  track  rails  on 
hand,  which  they  are  willing  to  sell  to  their  con- 
struction department  at  a  price  of  from  $20  to  $30 
per  ton.  They  are  estimated  in  the  table  accom- 
panying Figure  58,  to  cost  $40  per  ton,  or  2  cents 
per  pound,  placed  in  position.  Only  a  sufficient 
thickness  of  concrete  is  used,  to  completely  embed 
the  rails  and  hold  them  securely  in  position.  The 
strength  of  the  concrete  is  considered  only  by  allow- 
ing a  flange  stress  of  10,000  pounds  per  square  inch 
on  the  metal,  which  is  20  per  cent,  greater  than 
would  be  permitted,  if  the  concrete  filling  were  ab- 
sent. This  type  of  bridge  is  going  out  of  favor,  not 
only  because  it  is  not  economical,  but  also  because 
there  is  no  provision  for  resisting  shearing  stresses. 
Bridge  decks  so  constructed  have  excessive  deflec- 
tion, and  the  concrete  frequently  cracks  and  falls 
away  from  the  rails,  leaving  the  steel  exposed. 

If  loads  were  carried  by  the  bending  resistance  of 
the  concrete  and  rails  used  only  for  the  purpose  of 
reinforcement,  these  rails  would  then  be  spaced 
from  2  to  3  feet  apart.  The  best  modern  practice 
in  the  use  of  railtop  trestles  and  culverts  is  to  adopt 
a  mean  between  these  two  extremes,  and  use  slabs  of 
concrete  18  inches  in  thickness,  reinforced  with  old 
60-pound  rails  spaced  as  follows : 

For  6-foot  span,  place  rails  18  inches  apart  on  cen- 
ters. 


•35 


Size  of 
Beams 


1  1 


I   i   i 
%   s   s 


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234 


CONCRETE    CULVERTS    AND    TRESTLES.      235 

For  8-foot  span  place  rails  10  inches  apart  on 
centers. 

For  10-foot  span  place  rails  6  inches  apart  on  cen- 
ters. 

Design  B.  Figure  59.  In  this  design  beams  are 
placed  15  inches  apart  on  centers,  and  are  suf- 
ficiently heavy  to  carry  the  entire  load  by  the  bend- 
ing resistance  of  the  beams.  No  reliance  is  placed 
upon  the  concrete  excepting  that  a  working  fibre 
stress  on  the  metal  of  12,000  pounds  per  square  inch 
is  assumed,  which  is  greater  than  would  be  used,  if 
the  concrete  were  absent.  The  beams  are  firmly  em- 
bedded in  concrete  with  a  minimum  thickness  of  3 
inches  beneath  the  beams,  and  a  similar  depth  of 
concrete  above  the  beams  at  the  gutter.  The  upper 
surface  of  the  concrete  slab  is  sloped  from  the  gut- 
ter up  to  the  center  sufficiently  to  drain  the  water 
to  the  gutter  and  prevent  it  from  soaking  into  and 
disintegrating  the  concrete. 

Design  C.  Figure  60.  There  is  no  concrete 
whatever  in  connection  with  this  design.  It  is  one 
of  the  common  forms  of  short-span  railroad  bridges, 
and  the  table  of  sizes,  weights  and  estimated  costs 
is  given  for  comparison  with  the  cost  of  reinforced 
concrete  designs.  The  type  of  bridge  is  inferior  to 
the  concrete  designs  because  of  their  open  decks. 
An  open-deck  bridge  is  a  weak  place  on  a  perma- 
nent roadway.  If  a  train  is  derailed  on  a  solid  deck 
bridge,  the  chance  of  injury  either  to  the  train  or 
structure  is  less  than  when  derailment  occurs  on  an 
open  deck  bridge. 


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238        CONCRETE   BRIDGES   AND   CULVERTS. 

Design  D.  Figure  61.  This  type  is  similar  to 
Design  B,  but  differs  from  it  in  having  a  sufficient 
thickness  of  concrete,  reinforced  with  steel  beams, 
to  carry  the  entire  loads  by  the  bending  resistance 
of  the  concrete  slab.  The  steel  beams  are  covered 
on  the  lower  side  with  a  2-inch  layer  of  concrete. 
The  lower  two  inches  only  of  the  steel  beams  arc 
considered  effective  as  tension  metal,  for  concrete 
reinforcement.  Beams  are  spaced  about  18  inches 
apart  on  centers.  Piers  have  corbels  and  in  propor- 
tioning the  thickness  of  the  slabs  the  effective  span 
length  is  assumed  one  foot  shorter  than  the  actual, 
because  of  the  presence  of  these  corbels. 

Design  E.  Figure  62.  This  is  a  reinforced  con- 
crete trestle  design,  both  span  and  piers  having  rod 
reinforcement.  In  the  two  previous  pier  designs, 
reinforcing  steel  is  omitted,  but  for  Design  E  one- 
half  inch  square  rods  are  placed  18  inches  apart 
both  horizontally  and  vertically.  These  rods  serve 
not  only  to  prevent  cracks  from  change  of  tempera- 
ture, but  also  resist  any  tensile  stresses  which  might 
occur  in  thin  piers,  due  to  the  sudden  stopping  of 
heavy  trains  on  the  bridge.  The  spans  are  slab  con- 
struction, with  a  10-inch  slab  for  6-foot  span,  in- 
creasing to  36  inches  for  a  24-foot  span. 

Design  F.  Figure  63.  Like  the  previous  one, 
this  design  is  reinforced  entirely  with  rods,  but  is  a 
combination  of  beam  and  slab  construction.  Longi- 
tudinal concrete  beams  are  placed  10  feet  apart  in 
the  clear,  and  to  these  loads  are  transmitted  by 
means  of  18-inch  transverse  slabs,  carrying  the 


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242        CONCRETE   BRIDGES   AND    CULVERTS. 

track  and  ballast.  The  side  beams  are  each  2  feet 
in  width,  while  the  center  beam  is  4  feet.  The  load 
per  lineal  foot  on  the  side  beams  varies  from  8,500 
pounds  for  a  10-foot  span  to  9,300  pounds  for  a  2-4- 
foot  span. 

Designs  G  and  H.  Figures  64,  65.  These  are 
designs  for  single  track  trestles,  similar  to  E  and 
F  already  described.  They  differ,  however,  in  that 
G  and  H  have  a  3-foot  depth  of  earth  and  ballast 
filling. 

Comparative  Trestle  Costs. 

The  comparative  costs  for  the  foregoing  trestle 
spans  for  both  single  and  double  track  structures 
is  given  on  the  chart,  Figure  66.  The  horizontal 
ordinates  represent  clear  spans  in  feet,  while  the 
vertical  ordinates  give  the  costs  in  dollars  for  a 
complete  span,  not  including  piers.  This  chart 
clearly  shows  that  reinforced  concrete  trestles  of 
the  types  marked  E  and  F  with  rod  reinforcement 
are  more  economical  than  any  other  form  of  perma- 
nent trestle,  with  solid  roadway.  The  chart  shows 
further  that  reinforced  concrete  railroad  trestle 
spans  of  slab  constructions  are  economical  for  single 
track  in  spans  up  to  14  feet,  and  for  double  track 
in  spans  up  to  20  feet.  Above  these  lengths  the 
economic  form  of  span  is  a  combination  of  beam 
and  slab. 


Comparative  Cost  of  Short  Span  Bridges. 


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243 


INDEX. 


Page 

Abutments   ...55,  57,  148 

Movements  of  10 

Rankine's    Rules    for 58 

Trautwine's   Rules    for 55 

Abutment  Piers   11,   54,   70 

Trautwine's    Rules    for 55 

Adda    River    Bridge 80 

Adhesion,    Concrete    to    Steel 

108,   114,  116,   126,  186 

Advantages   of   Masonry 1 

Aisne  River  Bridge 176 

Almendares,    Cuba    Bridge...  97 

Augustus,  Bridge  of 3,  75,  76 

Anthony    Kill    Bridge 97 

Anderson.    L.    W 169 

Approximate   Computations..  32 

Aqueduct    of   Vejus 106 

Arcade — Spandrels    19 

Arch  Ring,  Thickness  of    50,  51 

Architectural  Design  100 

Area  of  Arch  Ring,  Required  69 
Atlantic  Highlands  Bridge..  178 
Atlanta,  Georgia,  Viaduct. .  .189 
Auckland,  New  Zealand, 

Bridge    80 

Austell,   Georgia,   Bridge 178 

Austrian   Experiments    105 

Avranche,    France,    Bridge.. 174 

Backing   52 

Baker's     Masonry    Construc- 
tion     59,    218 

Balustrade    187 

Batter   of  Piers 150 

Bearing  Power  of  Soils 59 

Bellefield    Bridge,    Pittsburg.   18 

Beam  Bridges   181,   183 

Advantages  of   183 

Cost    of    185 

Design   of 185 

Bending  Moments    133,135 

Biddle,   Col.    John 89 

Binnie     96 

Big      Muddy      River      Bridge 

17,   60,   89,   116 

Blome,   Rudolph    S 163 

Block  Structures   7 

Bond,    Mechanical    108 

Contractors'    157 

Boston,    Bridges    in 63 

Borrodale    Bridge    95 

Bormida   Bridge,   Italy 174 

Bosnia    176 

Boulder,  Col 178 


Page 

Boulder  Faced  Bridge.    166,   168 
Brookside    Park,    Cleveland..  97 

Brick   Arches ' 1 

Brick,    Strength    of 34 

Brooklyn,    Seeley   St.    Bridge.176 

Brunei    30 

Brown,   Wm.  H 98 

Building  Lintels    5 

Burr,  Wm.   H...80,   147,   159,   179 

Bush,   Lincoln   96,   98 

Buda  Pesth  176 

Cain,  Prof.  Wm 128 

Carriage    Travel    Loads 123 

Cantilever,    Action    of 5 

Concrete    10 

Caius    Flavius,    Bridge    Built 

by  74 

Casey,  E.   P.,   Architect.  .87,  159 

Canada  Creek  178 

Carter   98 

Cartersburg,  Ind 176 

Canal  Dover,   Ohio 176 

Cedar  Rapids,  Iowa 176 

Centers 7 

Chester   Bay    176 

Charley   Creek    178 

Chicago  Park  Bridge. ..  .169,  172 
Chatellerault,  France, 

Bridge     174 

Church,    Prof.    I.    P 42 

Cincinnati    Park    Bridge 104 

Cleveland,  Rocky  River 

81,   82,   83,    84,   95 

Colfax  Ave.,   So.  Bend 176 

Columbia  Park,  Lafayette. .  .178 

Courtwright,    P.   A 179 

Composition  of  Arches 1 

Concrete    120 

Cost       of       Solid       Concrete 

Bridges   63 

Re-Concrete  150 

Slab  Bridges   183 

Beam     185 

Piers    183 

Concrete     Steel     Engineering 

Co 163 

Como  Park,   St.   Paul 

61,   163,   167,   178 

Conjugate  Pressures. .  .4,   31,   67 

Continuity   of  Arch 7 

Colonnade  Spandrels 19 

Computations,  Approximate..  32 


245 


246 


INDEX. 


Page 

Cooper's  Engine  Loading 

49,   197,   229 

Connecticut  Ave.  Bridge 

60,  87,  88,  95 

Competitive  Designing  lot 

Corrugated  Bar  118 

Cracks    107 

Cruft    St.    Bridge,    Indianap- 
olis  178 

Crum  Elbow  Creek 178 

Crittenden,   H.    M 175 

Crown  Thrust   39,   40,  43 

Crown    of    Arch.,    Rise    and 

Fall    10 

Thickness    14 

Radius    15 

Filling  Depth  of 16.   67 

Crushing  of  Arch  Blocks,  33    34 

Cut   Water    on    Piers 150 

Cunningham,  A.  O 177 

Culverts     189 

Required  openings  for 191 

Box    194 

Tables  of 205,   207,   209,   211 

Cost  Chart  213 

Side  Walls   215 

Comparative  Cost  216 

Comparative    Cost    Chart.. 217 
Other  Common  Forms  of.. 219 

Curves  for 8 

Cushion,  Filling  as 16 

Cup  Bars 118 

Danville  Bridge    72,  97 

Danube  River  Bridges 95 

Dayton,  Ohio 174,  176 

Des  Moines  Bridge 63,  176 

Detroit    Ave.    Bridge,    Cleve- 
land      64 

Cost  of 81,  82,  83,   84,  95 

Development       of       Concrete 

Bridges    102 

Design,   Ultra  Refinement  in     7 
General,   of  Re-Concrete. .  .136 

Diversity   of    18 

Beam  and  Slab  Bridges. .  .185 

Dean,  John  161,  179 

Delaware  River  Bridge 95 

Decize,    France,   Bridge 174 

Decatur,  111.,   Bridge 176 

Decorah,  Iowa,  Bridge 176 

Derby,   Conn.,  Bridge 178 

De  Mollins,   M.   S 175 

De  Palo,   Michael 175 

Deck,    Kind  of 138 

Deck  Bridges,  Preference  for.108 

Diversity  of  Design 18 

Diamond  Bars 118 

Douglas,  W.  J 81,  89,  166,  177 

Drainage  of  Arches 52 


Page 

Duane,   W.  M 98,   179 

Earth  Slopes   5 

Eads    Bridge,    St.    Louis 145 

Economic  Span  Lengths 230 

Edmonson  Ave.   Bridge 95 

Eden  Park,   Cincinnati.  .104,  178 

Elastic  Theory   128 

Electric   Car  Loads 123 

Ellipse    8 

lo    Draw    20 

Elliptical   Intrados    145 

Emperor  Augustus   4,  76 

Embankments,  Loads  from.. 

5,    30 

Emperger,  Von   ....104,  177,   179 

Empirical   Rules    139 

Emerichsville    174 

Engine  Loading — 

Cooper's  E-50  49 

Estimating   154 

European  Practice   10 

External  Loads  and  Forces  4,  29 

Expansion 60 

Expansion   Joints    148 

Expanded  Metal    118 

Eyach  River   Bridge 97 

False  Work,   Removal   of 11 

Fall  Creek    178 

Felgate,    A.    M 85,    96 

Filling-Crown    16 

Load  from   30 

Over  Elliptical  Arches 32 

Earth    32 

Finish,  Surface 60 

Five      Centered      Arch,      To 

Draw   22 

Merits  of 145 

Fire  Insurance  157 

Floor  Renewals    2 

Fluid  Pressure  8 

Flat  Arches  107 

Floors   107 

Fleischman,  Eduard 98 

Florida   178 

Forms  8 

Forms,    How   ti   Draw 20 

Selection  of  Most  Suitable.  27 

Cost  of 154 

Forces,  External   29 

Polygon  of 39 

Foundations     58 

Fort,  E.  J 177 

Fort   Snelling,    Concrete   De- 
sign     80,    153 

Frankfort  Creek  Bridge 97 

Friction,  Sliding 33 

Franklin  Bridge,  Forest  Park 

161,   162,  178 

Funicular  Polygon  67 


INDEX. 


247 


Page 

Gary,  Ind.,  Bridge 163,  1G5 

Galicia  Bridge  176 

Garfield  Park  Bridge,  Chi- 
cago   169,  172 

General  Outline  8 

Germantown  Bridge 82 

General  Design  of  Re-Concr. 

Bridges  136 

Geisel  Construction  Co 161 

Geostatic  Arch,  To  Draw... 

24,  29 

Glendoin,  Cal.,  Bridge 178 

Golden  Gate  Park  Bridge... 

61,  104 

Granite,  Strength  of 34 

Green  Island,  Niagara ...  .61,  174 

Gruenwald 80,  95 

Grand  Rapids  Bridge 

166,  169,  170,  176 

Grand  River  174,  176 

Grand  Tower.  Ill 89,  95 

Grand  Ave.,  Milwaukee 

119,  126,  143 

Green,  Prof.  Chas.  E 128 

Guaya  River  173 

Gwynns  River 95 

Hawgood.  Henry  91,  98 

Hammond,  A.  J 163 

Hainsburg  Bridge  97 

Height  of  Bridges 12 

Headroom  Under  Bridges...  66 

Heyworth  J.  O 163 

Hewett,  W.  S 166,  179 

Herkimer,  N.  Y 178 

Hinges  7 

Hinged  Arches  ..10,  129,  132,  140 
History  of  Concrete  Bridges.  .102 

High  Tension  Steel Ill 

Highway  Beam  Bridges 181 

Hilty  179 

Hibbard.  M.  S...., 179 

Huntington.  Ind 174 

Hudson  Memorial  Bridge 

72,  77,  78,  95 

Hudscn  River  Bridge,  Sandy 

Hill  153 

Hydrostatic  Arch,  How  to 

Draw 24,  26,  27 

Hyde  Park  on  Hudson 176 

Idaho,  Bridge  in 48 

111.    Cent.    R.    R.    Bridges.... 

17,  60,  89,  116 

Standard   Culverts    221 

Illinois  River  Bridge,   Peoria.149 

Illustrations  of  Bridges 71 

lller  River  Bridge 95,  141 

[mpact 127,  229 

Imnau,  Bavaria  97 

Interlaken,    Minneapolis    ..,.178 


Page 

Intermediate  Piers   69 

Ingersoll,    C.    M 80 

Intrados   Form    145 

Inzighofen    Bridge    95 

Indianapolis,   Morris   St 174 

Meridian    St 178 

Illinois  St 178 

Cruft  St 178 

Northwestern   Ave 178 

lola.   Kansas    178 

Irrigation    Canal,    in    Idaho..   48 
Isar  River  Bridge. 95 

Jacksonville,  Florida,  Bridge. 178 

Jacaquas  River  Bridge 174 

Jamestown  Exposition 

Bridge' 59,  160,  161,  174 

Jefferson  St.,  South  Bend... 

161,  164,  174 

Jeup,  B.  J.  T 179 

Joints,  Expansion  148 

Tension  in  7 

Judson  175,  17d 

Kahn,  Julius 179 

Bar   118,  120 

Kansas  River    174 

Kalamazoo  River .  .178 

Keepers    175 

Kempten   Bridge    95,   141 

Key  West,  Florida 97 

Kissinger  Bridge   140 

Kirchheim    Bridge    97 

Kresno,   Galicia   176 

Laibach,  Austria  174 

Lake   Park,    Milwaukee 174 

Law  of  Lever 131 

Larimer    Ave.,    Pittsburg. . . .   97 

Lawrenceburg  Trestle    190 

Lansing,  Mich 174 

Lautrach,  Germany   95 

Leffler,    B.    R 175 

Leonard,    John    B '....117 

Length  of  Span,  Economical.  13 

Lea,  A.  B 85 

Leibbrand,  Max    96,   98 

Lindenthal  Gustav  177 

Lima.    Ohio    178 

Liquid  Pressure 5 

Lintels    5 

Line  of  Resistance,  Indefinite     7 

Determination  of 36 

Position  of   42 

For  LTniform  Load 43 

For  Partial  Load   45,  129 

Linear  Arch  9,  28 

Limestone,    Strength    of 34 

Liability  Insurance    157 

Logansport,  Ind 178 

London,    Ohio 178 


248 


INDEX. 


Page 

Loire  River   174 

Local  Labor 2 

Loads    121 

Load,  Contour  Reduced 41 

Adjustment    to    Form 19 

External    29 

Uneven   68 

On  Culverts  195 

Long  Key  Viaduct 97 

Luten,  D.  B 175,  177,  179 

Truss     118 

Luten's  Empirical  Formula.. 224 

Luxemburg  80,  144 

Mary  River   178 

Maryborough  Bridge   178 

Maumee   River  Bridge 176 

Marsh   Bridge  Co 177 

Maintenance    2 

Masonry,   Strength  of 6 

Mathematical        Theory        of 

Arch 32 

Materials,   Strength  of 34 

Marachina  River,   Italy 76 

Main  River 97 

Main  Street  Bridge,  Dayton..  176 

Mclntyre,    Charles    179 

Melan,    Prof.   J 103,    175 

Merits  of  Concrete  Bridges.. 

107,  103 

Metal  Reinforcement Ill 

Medium  Steel    Ill 

Meyer's  Formula  194 

Mechanicsville  Bridge 97 

Mercereau  179 

Milwaukee  Viaduct 119 

Miltenburg    97 

Mississippi   River    97 

Middle  Third  of  Arch  Ring. . .   33 

Miners   Ford    178 

Mission    Ave.,    Spokane 178 

Miami  River 174,  176 

Monroe  St.   Bridge,   Spokane.  72 

Moisseiff,   L,    S 80 

Morsch,  Prof.  J 81,  96 

Morrison,  George  S 80,  96 

Monier,    Jean    103 

Morris    St..    Indianapolis 174 

Monolith  Frame  118 

Murray,  Paul  R 177 

Multi-Center  Curve   9 

To  Draw 20,  21 

Municipal   Art  League 78 

Munderkingen   85 

Navier's  Principle 24 

National  Zoological  Park 61 

New    York    Bridges 73 

New    Zealand,    Longest    Ma- 
sonry  Span    80 


Page 

Neckar  River  85 

Bridge     95 

Nelson   St.   Viaduct,   Atlanta. 189 

Newark,    N.    J 174 

New    Goshen,    Ohio 176 

Newton,  Ralph  E 175 

Neckarhausen,  Germany   ....  95 
Niagara  Falls,  Green  Island.. 

61,   174 

Nimes,    Aqueduct,    France. .  .105 

Noise,  Absence  of 107 

Northern   Pacific   R.    R     Cul- 
verts     222 

Nobel,  Alfred 98 

Oconomowoc.  "Wis 178 

Olive  Ave.   Bridge,   Spokane..  178 

Open   Spandrels    17 

Ornamental   Bridges    99 

Osborn.    Frank    C 17!» 

Outline,   General   139 

Parkhurst,  H.  W 91,  96 

Park  Bridge  Design 99 

Pantheon,  Rome   106 

Painting    2 

Painting   Reinforcing   Steel..  116 

Parabolic  Arch,  To  Draw 

23,   134,  147 

Pavement    16 

Pavement    Slabs    215 

Pavement  Ties  56 

Paulins    Kill    97 

Painsville,   Ohio    1 7'4 

Paterson,   N.   J 176 

Plainwell,    Michigan    178 

Passaic  River    176 

Partial  Load,  Line  of  Press- 
ure     45,    68 

Peoria  Bridge   149 

Pelham    Bridge    176 

Peru,  Ind.,  Bridge 176 

Pena   River    174 

Philadelphia   85,  86,   87,   95 

Philadelphia,    Tacony   Creek.   97 

Piney  Creek   18,   97.  142 

Piers,  Thickness  of.. 66,  148,  150 

Cost  of 183 

Abutment    11,    54,    70 

Intermediate 53,  69 

Pier  Thrust,    To    Balance 14 

Pine    Creek    ITS 

Pittsburg,    Pa 9 1 

Piles,    Batter  and  Plumb 59 

Load    on    59 

Playa    Del    Rey 174 

Plainfield,    Ind 178 

Plauen,    Germany    80,    85 

Potomac  Memorial   Bridge... 

147,   153,  159 

River     87 


INDEX, 


249 


Page 

Portland,   Pa.,  Bridge 95 

Porto    Rico     174,    178 

Portugal     174 

PollusKy,  Cal 176 

Pont    Du   Gard 105 

Ponte  Rotto,  Rome 3,  73,  74 

Pons  Aemilius 74 

Palatinus   74 

Lapideus    74 

Polygon,  Force   39 

Pole    39,    67 

Distance     43 

Point   of   Rupture 50 

Pressure  Curve,  To  Deter- 
mine    36 

Pressure    of    Liquid 5 

Sand    5 

Pressure     on      Surfaces,      To 

Find     42 

Prices,   Estimating   155 

Preservation   of   Steel 114 

Pyrimont,  France   174 

Quimby,    Henry   M 87,    98 

Quantities,  Approximate   158 

Railing   187 

Ralston,  J.  C 179 

Rankine's  Rules  for  Crown 
Thickness  14 

Pier    Thickness    53,    66 

Rankine's  Method  of  Draw- 
ing Hydrostatic  Curve.. 
26,  27 

Rules  for  Abutment  Thick- 
ness       58 

Railroad    Bridges 2,    3 

Reinforced    Concrete    Arches, 

Costs     150 

Table   of    

..174,    175,    176,    177.    178,    179 

Part  II   100 

Advantages    of    106 

Reynolds     175 

Reduced    Load    Contour 41 

Reilly    and    Riddle 87 

Reinforcing    Steel 101,    111 

Reinforcing     Systems     117 

Retaining   Walls    122 

Rhone    River     174 

Riverside,   Cal,   91,   92,   93,   94,   97 

Riboud     177 

Richmond,   Va.,   Trestle  154,   188 

Rise    of   Arch 8.    40,    66 

Rise    and    Span 12 

Ribbed    Arch 129,    142 

Rockville    Stone    Arch 61 

Roxborough,    Pa 87 

Rocky  River  Bridge,   Cost   of 

64,    95.    80,    81,    82,    83,    84 

Rotation    of    Arch    Blocks..  33 


Page 

Rock  Skewbacks  28 

Rock  Creek  87,  176 

Rome,  Ponte  Rotto 3,  73,  74 

Roman  Arches  8 

Length  of  Spans 

13,  73,  74,  75,  76 

Rusche,  J.  P 169 

Rupture,  Point  of 50 

Santa  Ana  Bridge,  Cal 

55,  91,  9^,  93,  94,  97 

San  Gabriel  River  Bridge..  178 

San  Joaquim  River 176 

San  Francisco  Bridges 61 

Sangamon  River  176 

Sandy  Hill,  N.  Y 153,  178 

Sarajero,  Bosnia  176 

St.  Paul  Bridges  174 

St.  Joseph  River 174 


St.    Louis,    Eads    Bridge.. 


.145 


Sand    Pressure 

Sandstone,     Strength    of .  .  .    .   34 

Scofield    Engineering    Co.. 

161,     175 

Schillinger    Bros 85 

Seeley   St.    Bridge,   Brooklyn.176 

Schenley    Park    Bridge 18 

Schemers    Theorem 32 

Semi-Circular    Arch    8 

Senators'    Bridge    74 

Segmental    Arches     8 

Culvert    Arches     14 

Selection     of    Most     Suitable 

Form     27 

Sewer    Arch    32 

Simpson    and    Wilson,    Engi- 
neers       96 

Sitter    River    81 

Skewback,    Rock     28 

Slab    Table    for    Culverts 198 

Slabs,     Cost    of 200 

Slab    Reinforcing    118 

Slab   Arches    129 

Slab      Bridges,      Table     with 

Costs     183 

Slab    and    Beam    Bridges 198 

Slopes,    Earth    5 

Sliding   of   Blocks 33 

South    Bend,    Ind 174 

Soissoins.     France     176 

Solid    Arches,    Tables    of 

95,   96,   97,   98 

Soil,    Bearing    Power    of 59 

Spokane,    Mission    Ave 178 

Olive   Ave 178 

River     178 

Monroe    St 79.    72,    97 

Spandrels    147,    16,    17 

Spandrel    Columns     138 


250 


INDEX. 


Page 

Spandrels,     Arcade     or     Col- 
onnade       19 

Spandrel    Filling    28,    37 

Springs,    Low    149 

Position    of    10 

Span     12 

Spuyten    Duyvil    Creek    ..78,    95 
Stony     Brook     Bridge,     Bos- 
ton        63 

Steyr,    Austria    145,    174 

Stability    Requirements.  .33,    136 

Stockbridge,     Mass 176 

Stein-Teufen    Bridge     173 

Steel    Reinforcement     ..101,    111 
Strength       of       Re-Concrete 

Arches     107 

Stirrups     117 

Survey    for    Bridge 157 

Surface    Finish    60 

Switzerland    Bridge     81 

Tacony    Creek    97 

Telephone    at    Bridge 157 

Terre    Haute     178 

Test    Loads     1 

Tension    in    Joints 7 

Tension    in    Concrete 114 

Teufen    Bridge.     Switzerland.173 
Temperature    Stresses.  .124,    150 

Thickness    of   Arch    Ring 135 

Thebes    Bridge     97 

Thames     River     Bridge 95 

Thacher,    Edwin 18,    119,    177 

Thacher    Bars    118 

Three      Centered     Arch,      To 

Draw     20 

Merits     of     145 

Theory,     Mathematical     32 

Theory    of    Arches 126 

Thrust      on      Piers,      Unbal- 
anced        53 

Ties    on     Bridge    Floors 107 

Ties,     Pavement     56 

Tiber   River.    Rome 74 

Topeka   Bridge,    10,    31,    149,    174 

Trestles    1S9,    228 

Economic    Spans     200 

Rail    Tops 230,    231,    232 

Beam    Tops    233.    235 

Steel   Beam   Decks 234.  23r, 

Beam    Tops    236,    238 

Slabs,    Rod    Reinforcement. 

237,     238,    240 

Beams,       Rod      Reinforce- 
ment     238,    239 

Comparative    Costs    242 

Chart     243 

Temporary     48 

Trinidad,    Col 178 

Trim    Creek    .  ..178 


Page 

Truss    System    4 

Trautwine's   Rule  for  Crown 

Thickness     14 

Abutment    Piers    55 

Travertine,    Used    in    Rome    74 

Trial    Method    of    Design 146 

Tubesing,    W.    F 169     177 

Tuscarawas    River    .  174 

Turner,    F.    M 175    '177 

Turner,  C.  A.  P 144,  175 

Tunnel    Arch    5 

Twisted    Rods us 

Twisted    Lug    Bars llg 

Tyrrell,      H.      G.,      Concrete 

Bridges    Designed    by 

48,    62,    99,    167 

Tyrrell,       M.       K.,       Designs 

by    182,    184 

Ultra-Refinement    in    Design.     7 

Ultimate   Values    34 

Ulm,    Germany    95 

Uncertainty    of    Masonry    4,    129 

Unit    Pressures    33 

On    Surface.    To    Find 42 

Working     35 

Ultimate    and    Working. .  .125 

Unit    Reinforcing    Frame 118 

Uneven   Loading    68 

Unsymmetrical    Arch     139 

Various   Forms,    To    Draw...   20 

Values,     Ultimate     34 

Varying:  Span   Lengths    13 

Vauxhall,    London     95 

Vermillion         Riv.         Bridge, 

Wakeman    9.    30,   174 

Vermillion  Riv.   Bridge,  Dan- 
ville     72,   97 

Vejus.    Aqueduct    of 106 

Venice.    Cal 169.    171 

Viaducts    over    Yards 13,    66 

Vibration.     Absence    of 107 

Vienne    River     174 

Von   E'mperger    104,    177,    179 

Washington,      D.      C.,      Rock 

Creek     176 

Connecticut    Ave 

87,    88,    166,    168 

Washington    St.,    Daj'ton. . .  .176 

Waterloo,    Iowa     178 

Wabash.   Ind 140,    178 

Waterville,     Ohio     176 

Wayne    St..    Peru.    Ind 176 

Walker 177 

Wakemen.   Ohio    9.   30,  174 

Walls.     Thickness    of    Span- 
drel      19 

Loads    on    29 

Waterproofing    52,    216 


INDEX. 


251 


Page 

Watersoaking    110,   115 

Waterway,    Width   of 56 

Walnut    Lane    Bridge,     Sur- 
face  Finish    60 

Cost   of    ....64,    142,    80,    85,   95 
Warren,   Whitney,   Architect.  80 

Watson,  Wilber  J 85,  175 

Waidhofen    174 

Wells,    W.    H 179 

Webster,    George    S..85,    96,    98 

Whited,  Willis    ...; 98 

Wildegg.   Switzerland    174 

Wise,    C.    R 177 

Wilson.    George    L 179 

Widening    Concrete    Bridges.     3 


Page 
Window  Arches,    Load  on...     6 

Wire   Net   Reinforcement 118 

Width    of    Deck 138 

Wing   Walls    149 

Wissahickon   Creek    95 

Workmanship    7,   110 

Working  Units   35,  106 

Wood     Bridges,     Competition 

with     102 

Wunsch,    Professor    116,    177 

Wyoming      Ave.,       Philadel- 
phia       97 

Yellowstone    Park    Bridge...  174 
Zesiger,   A.   W 98 


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book  ever  written  on  this  subject.  It  is,  in  fact,  a 
combination  of  several  books  in  one — all  original, 
carefully  vvritten  and  up-to-date.  It  has  200  working 
drawings  of  bridges,  bridge  piers  and  culverts;  60 
working  drawings  of  sewers,  water  mains  and  reser- 
voirs; 30  working  drawings  each  of  retaining  walls 
and  dams;  200  working  drawings  of  buildings  and 
foundations,  including  shops,  roundhouses,  etc. 

It  has  more  text  pages,  more  drawings  and  more  tables  of  test 
data  on  concrete  and  reinforced  concrete  construction  than  any 
other  book  ever  published.  No  other  book  on  concrete  contains 
one-tenth  so  much  of  the  very  latest  data  on  tests,  theory  and 
practice. 

9O6    pages,     715    illustrations, 
7O  tables;  $5.OO  net,  postpaid. 

16-page  Table  of  Contents  free. 

The  Myron  C.  Clark  Publishing  Co. 

355  Dearborn  St.,  Chicago 


Theory  and  Design 

OF 

Reinforced   Concrete   Arches 

A  Treatise  for  Engineers  and  Technical 
Students. 

By  ARVID  REUTERDAHL,  Sc.  B.,  A.  M. 

Chief  of  Bridge  Department,  Engineering  Department, 

City  of  Spokane,  Wash. 

The  books  which  have  heretofore  been 
published  on  this  subject  are  either  so 
mathematically  abstruse  or  leave  so 
much  to  the  reader  to  demonstrate  for 
himself,  that  they  are  of  little  value  to 
the  general  practitioner  or  to  the  tech- 
nical student  whose  mathematical  ability 
is  not  of  exceptional  order.  These  objec= 
tions  have  been  overcome  in  this  book. 
Every  principle  is  explained  thoroughly — 
there  are  no  missing  steps  in  the  mathe= 
matics. 

The  book  should  be  in  the  hands  of  every  engineer 
who  has  concrete  bridges  to  design  and  of  every  student 
of  the  theory  and  practice  of  concrete  bridge  design. 

Cloth,  6x9  inches;  132  pages;  numerous  diagrams  and  tables; 
price  $2.00  net,  postpaid. 

THE  MYRON  C.  CLARK  PUBLISHING  CO. 

355  Dearborn  Street,  Chicago 


Reinforced  Concrete 

A  Manual  of  Practice 

By  ERNEST  McCULLOUGH,  C.  E. 

This  book  was  written  for  the  practical  concrete 
worker — the  man  on  the  job — who  has  not  the  re- 
quirements of  statics  and  the  theories  of  the  mathe- 
matician at  his  tongue's  tip  but  who  desires,  in 
plain  words,  the  fundamentals  of  correct  design  and 
the  practice  of  sound  and  economical  construction 
work. 

Cloth,  Sx7f  inches;  136  pages;  illustrated; 
price  $1.50  net,  postpaid. 


Field  System 

By  FRANK  B.  GILBRETH 

This  book  was  written  by  one  of  the  largest 
general  contractors  in  the  world,  and  contains  nearly 
200  pages  of  rules  and  instructions  for  the  guidance 
of  his  foremen  and  superintendents.  It  is  the  out- 
growth of  over  twenty  years  of  experience  in  the 
contracting  business,  and  embodies  scores  of  sug- 
gestions for  economizing  and  for  increasing  the  out- 
put of  the  men  on  the  job.  Mr.  Gilbreth  is  the  con- 
tractor who  made  the  "Cost-plus-a-fixed-sum-con- 
tract"  famous;  in  doing  so,  he  has  likewise  made 
famous  Gilbreth's  "Field  System,"  only  a  few  ex- 
cerpts from  which  have  heretofore  appeared  in  print. 

One  thousand  copies  were  sold  in  the  first  ten 
days. 

In  making  public  his  "Field  System"  Mr.  Gilbreth 
is  performing  a  service  to  the  public  that  is  com- 
parable with  the  action  of  a  physician  in  disclosing 
the  secret  of  his  success  in  curing  a  disease.  The 
disease  that  Gilbreth's  "Field  System"  aims  to  cure 
is  the  hit  or  miss  method  of  doing  contract  work. 
System  supplants  slovenliness,  and  makes  sloth  an 
absolute  impossibility. 

200  pages,  with  illustrations;  bound  in  leather; 
price  $3.00  net,  postpaid. 

THE  MYRON  C.  CLARK  PUBLISHING  CO. 

355  Dearborn  Street,  Chicago 


H.  G.  TYRRELL 

CIVIL  ENGINEER 

Chicago,  Illinois 
Evanston,  Illinois 


DESIGNER  AND   ENGINEER 
FOR  ALL  KINDS  OF 

Bridges  and 


Structures 


Special  Attention  to  Selection 
of  Economic  Types 


UNIVERSITY  OP  CALIFORNIA  LIBRARY 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 


SEP  13  1915 


MAR  S    1S27 


JAN 


flPP  2  0  195. 


930 


30m-l,'15 


194738 


r 


